We study K-theory of continuous deformations of C*-algebras to obtain that their K-theory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz alge...We study K-theory of continuous deformations of C*-algebras to obtain that their K-theory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz algebras.展开更多
In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed fi...In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.展开更多
Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors constru...Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold.The authors show that for a finite group G and a G-equivariant stable almost complex manifold X,the G-invariant part of the stringy cohomology ring of(X,G)is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold[X/G].Similar result holds when G is a torus and the action is locally free.Moreover,for a compact presentable stable almost complex orbifold,they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.展开更多
This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and exampl...This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and examples.The convergence of local solutions is discussed.展开更多
Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the uni...Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.展开更多
All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as ...All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.展开更多
In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property(H).
Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of ...Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.展开更多
In this paper,we give a classification of real rank zero C^(*)-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C.
By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the ope...By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.展开更多
I. PREPARATION AND LEMMASWe start recalling theMain Theorem of Abresch. Given an isoparametric hypersurface in S<sup>n+1</sup> with g= 4, then the pair (m<sub>,</sub> m<sub>+</sub>...I. PREPARATION AND LEMMASWe start recalling theMain Theorem of Abresch. Given an isoparametric hypersurface in S<sup>n+1</sup> with g= 4, then the pair (m<sub>,</sub> m<sub>+</sub> )-w. r. g, we may assume that m<sub> </sub>≤m<sub>+</sub>, satisfies one of the three conditions below:展开更多
Let S be a semigroup with identity and zero,(S)the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω(...Let S be a semigroup with identity and zero,(S)the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω(S), where Ω(S)is the Loop category of(S),and the structure of K<sub>1</sub>S is given.展开更多
Let X be a finite CW complex, and let ξ be a real vector bundle over X. We say that ξ has a complex structure if it is isomorphic to the real bundle r(ω)underlying some complex vector bundle ω over X. Let M be a c...Let X be a finite CW complex, and let ξ be a real vector bundle over X. We say that ξ has a complex structure if it is isomorphic to the real bundle r(ω)underlying some complex vector bundle ω over X. Let M be a closed connected smooth manifold. We say that M has an almost structure if its tangent bundle has a complex structure.展开更多
Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the pers...Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.展开更多
In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Major...In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Majorana zero mode in the vortex core is neither a necessary nor a sufficient condition for the superconductor in question being topologically non-trivial.展开更多
Let A be an associative ring with identity, St_n(A) the Steinberg group of dimension n over A. The stable Steinberg group is the direct limit of the St_n(A) in a natural way. Several authors studied various normal for...Let A be an associative ring with identity, St_n(A) the Steinberg group of dimension n over A. The stable Steinberg group is the direct limit of the St_n(A) in a natural way. Several authors studied various normal forms for elements of St(A) and St_n(A) (cf.[ 3—7]).展开更多
Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commut...Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commutative rings. The present note extends the result of [2] to non-commutative rings and studies the decomposition of a finite Steinberg group over local rings.展开更多
In this paper we prove that for a fixed l, the number of multiplicative ψ<sub>k</sub>-module M=Z/p[y<sub>1</sub>,…,y<sub>1</sub>]/(Z/p[y<sub>1</sub>,…,y<sub>1&...In this paper we prove that for a fixed l, the number of multiplicative ψ<sub>k</sub>-module M=Z/p[y<sub>1</sub>,…,y<sub>1</sub>]/(Z/p[y<sub>1</sub>,…,y<sub>1</sub>])<sup>p+1</sup>with degy<sub>i</sub>=2b<sub>i</sub>, i=1,…, l, is finite, and for a fixed l, the unstable polynomial A<sub>p</sub>-al-gebras P(B)=Z/p[x<sub>1</sub>,…,x<sub>1</sub>] which are realizable are finite.展开更多
Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(...Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(Г)■zZ[1/p] when p = 2,3,5,7. As an application, we give the structure of K2(Z[G]) for G a cyclic p-group or an elementary abelian p-group.展开更多
文摘We study K-theory of continuous deformations of C*-algebras to obtain that their K-theory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz algebras.
基金Science and Technology Commission of Shanghai Municipality(STCSM)(Grant No.18dz2271000)Natural Science Foundation of Shanghai(Grant No.20ZR1416700)National Natural Science Foundation of China(Grant No.11931007)。
文摘In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.
基金supported by the National Natural Science Foundation of China(Nos.11501393,11626050,11901069)Sichuan Science and Technology Program(No.2019YJ0509)+1 种基金joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V.C.&V.R.Key Lab of Sichuan Province,by Science and Technology Research Program of Chongqing Education Commission of China(No.KJ1600324)Natural Science Foundation of Chongqing,China(No.cstc2018jcyjAX0465).
文摘Comparing to the construction of stringy cohomology ring of equivariant sta-ble almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds,the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold.The authors show that for a finite group G and a G-equivariant stable almost complex manifold X,the G-invariant part of the stringy cohomology ring of(X,G)is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold[X/G].Similar result holds when G is a torus and the action is locally free.Moreover,for a compact presentable stable almost complex orbifold,they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.
基金supported by a KIAS Individual Grant(MG083901)at Korea Institute for Advanced Studya POSCO Science fellowship。
文摘This is a set of lecture notes for the first author’s lectures on the difference equations in2019 at the Institute of Advanced Study for Mathematics at Zhejiang University.We focus on explicit computations and examples.The convergence of local solutions is discussed.
文摘Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.
基金supported by the National Natural Science Foundation of China(Nos.12171156)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property(H).
基金The bulk of this work was done during the first author’s tenure at University of Michigan and he was partially supported by NSF grant DMS 1807079 and NSF FRG grant DMS 1564457.
文摘Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.
基金supported by Northeast Normal University and National Natural Science Foundation of China(Grant No.11531003)supported by University of Toronto and National Natural Science Foundation of China(Grant No.11531003)+1 种基金supported by the Science and Technology Development Project of Jilin Province(Grant No.20190103028JH)National Natural Science Foundation of China(Grant Nos.11601104,11671167 and 11201171).
文摘In this paper,we give a classification of real rank zero C^(*)-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C.
基金This Work was supported by the National Natural Science Foundation of China(Grant No.10171014)the Natural Science Foundation of Fujian Province of China.
文摘By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
文摘I. PREPARATION AND LEMMASWe start recalling theMain Theorem of Abresch. Given an isoparametric hypersurface in S<sup>n+1</sup> with g= 4, then the pair (m<sub>,</sub> m<sub>+</sub> )-w. r. g, we may assume that m<sub> </sub>≤m<sub>+</sub>, satisfies one of the three conditions below:
文摘Let S be a semigroup with identity and zero,(S)the category of finitely generated projective S-systems.In this paper,the Whitehead group K<sub>1</sub>S of S is defined to be K<sub>0</sub>Ω(S), where Ω(S)is the Loop category of(S),and the structure of K<sub>1</sub>S is given.
文摘Let X be a finite CW complex, and let ξ be a real vector bundle over X. We say that ξ has a complex structure if it is isomorphic to the real bundle r(ω)underlying some complex vector bundle ω over X. Let M be a closed connected smooth manifold. We say that M has an almost structure if its tangent bundle has a complex structure.
基金supported by the National Natural Science Foundation of China(Nos.11771143,11831006,11420101001).
文摘Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.
基金supported by the Theory Program at the Lawrence Berkeley National Laboratory, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231
文摘In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Majorana zero mode in the vortex core is neither a necessary nor a sufficient condition for the superconductor in question being topologically non-trivial.
基金Project supported by the National Natural Science Foundation of China.
文摘Let A be an associative ring with identity, St_n(A) the Steinberg group of dimension n over A. The stable Steinberg group is the direct limit of the St_n(A) in a natural way. Several authors studied various normal forms for elements of St(A) and St_n(A) (cf.[ 3—7]).
文摘Sharpe once gave a beautiful 4-term decomposition LPLU for infinite Steinberg group; recently Li Fu-an has given a sufficient and necessary condition for 4-term decomposition LWLU of finite Steinberg group over commutative rings. The present note extends the result of [2] to non-commutative rings and studies the decomposition of a finite Steinberg group over local rings.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper we prove that for a fixed l, the number of multiplicative ψ<sub>k</sub>-module M=Z/p[y<sub>1</sub>,…,y<sub>1</sub>]/(Z/p[y<sub>1</sub>,…,y<sub>1</sub>])<sup>p+1</sup>with degy<sub>i</sub>=2b<sub>i</sub>, i=1,…, l, is finite, and for a fixed l, the unstable polynomial A<sub>p</sub>-al-gebras P(B)=Z/p[x<sub>1</sub>,…,x<sub>1</sub>] which are realizable are finite.
基金This work was supported by the National Natural Science Foundation for Young Scientists of China (Grant No. 11401412the National Natural Science Foundation of China (Grant No. 11771422)the Scientific Research Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant No. 18KJB110025).
文摘Let G be a finite abelian p-group,Г the maximal Z-order of Z[G]. We prove that the 2-primary torsion subgroups of K2Z[G]) and K2(Г)are isomorphic when p ≡ 3, 5, 7 (mod 8, and K2(Z[G])■zZ[1/p] is isomorphic to K2(Г)■zZ[1/p] when p = 2,3,5,7. As an application, we give the structure of K2(Z[G]) for G a cyclic p-group or an elementary abelian p-group.