The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vect...The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.展开更多
In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.展开更多
The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-...The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.展开更多
It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrod...It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) ?andO(3,1) , based in admissible representations of U(1) , and SU(n)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of £-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.展开更多
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a v...SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a variety of ways,but it is still difficult to achieve a precisely located fault attacks at a low cost,whereas a Hardware Trojan(HT)can realize this.Temperature,as a physical quantity incidental to the operation of a cryptographic device,is easily overlooked.In this paper,a temperature-triggered HT(THT)is designed,which,when activated,causes a specific bit of the intermediate state of the SKINNY-64-64 to be flipped.Further,in this paper,a THT-based algebraic fault analysis(THT-AFA)method is proposed.To demonstrate the effectiveness of the method,experiments on algebraic fault analysis(AFA)and THT-AFA have been carried out on SKINNY-64-64.In the THT-AFA for SKINNY-64-64,it is only required to activate the THT 3 times to obtain the master key with a 100%success rate,and the average time for the attack is 64.57 s.However,when performing AFA on this cipher,we provide a relation-ship between the number of different faults and the residual entropy of the key.In comparison,our proposed THT-AFA method has better performance in terms of attack efficiency.To the best of our knowledge,this is the first HT attack on SKINNY-64-64.展开更多
We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we c...We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.展开更多
Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation: f(kx + y) + f(kx - y) = kf(x + y) + kf(x - y) + 2f(kx) - 2kf(x) in Banach mod...Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation: f(kx + y) + f(kx - y) = kf(x + y) + kf(x - y) + 2f(kx) - 2kf(x) in Banach modules over a unital Banach algebra.展开更多
In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd...In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module.展开更多
Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf mod...We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.展开更多
Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is ...In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.展开更多
The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensive...The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.展开更多
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf...In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.展开更多
基金Fundamental Research Funds for the Central Universities,China(No.2232021G13)。
文摘The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.
文摘In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.
文摘The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.
文摘It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) ?andO(3,1) , based in admissible representations of U(1) , and SU(n)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of £-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金supported in part by the Natural Science Foundation of Heilongjiang Province of China(Grant No.LH2022F053)in part by the Scientific and technological development project of the central government guiding local(Grant No.SBZY2021E076)+2 种基金in part by the PostdoctoralResearch Fund Project of Heilongjiang Province of China(Grant No.LBH-Q21195)in part by the Fundamental Research Funds of Heilongjiang Provincial Universities of China(Grant No.145209146)in part by the National Natural Science Foundation of China(NSFC)(Grant No.61501275).
文摘SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a variety of ways,but it is still difficult to achieve a precisely located fault attacks at a low cost,whereas a Hardware Trojan(HT)can realize this.Temperature,as a physical quantity incidental to the operation of a cryptographic device,is easily overlooked.In this paper,a temperature-triggered HT(THT)is designed,which,when activated,causes a specific bit of the intermediate state of the SKINNY-64-64 to be flipped.Further,in this paper,a THT-based algebraic fault analysis(THT-AFA)method is proposed.To demonstrate the effectiveness of the method,experiments on algebraic fault analysis(AFA)and THT-AFA have been carried out on SKINNY-64-64.In the THT-AFA for SKINNY-64-64,it is only required to activate the THT 3 times to obtain the master key with a 100%success rate,and the average time for the attack is 64.57 s.However,when performing AFA on this cipher,we provide a relation-ship between the number of different faults and the residual entropy of the key.In comparison,our proposed THT-AFA method has better performance in terms of attack efficiency.To the best of our knowledge,this is the first HT attack on SKINNY-64-64.
基金supported by NSF of China(11801117,11971315)the Natural Science Foundation of Guangdong Province,China(2018A030313268)partially supported by NSFof China(11801390).
文摘We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.
基金The NSF(11371307)of ChinaResearch Culture Funds(2014xmpy11)of Anhui Normal University
文摘Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
基金supported by the National Natural Science Foundation of China (10671013,60972089,11171022)
文摘Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation: f(kx + y) + f(kx - y) = kf(x + y) + kf(x - y) + 2f(kx) - 2kf(x) in Banach modules over a unital Banach algebra.
文摘In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module.
文摘Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
文摘We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.
文摘Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
文摘In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.
基金Supported by the National Natural Science Foundation of China(10871170) Supported by the Educational Minister Science Technology Key Foundation of China(108154)
文摘这份报纸,主要由一种新方法为模块 coalgebras 给结构定理,并且删除 Hopf 代数学 H 的相对极 S 是 bijective 的条件。
基金Supported by the Emphasis Supported Subject Foundation of Shanxi Province(20055026) Supported by the Emphasis Science Foundation of Yuncheng University(20060103)
基金Supported by National Natural Science Foundation of China(Grant No.51375059)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)+1 种基金Special Fund for Agro-scientific Research in the Public Interest of China(Grant No.201313009-06)National Key Technology R&D Program of the Ministry of Science and Technology of China(Grant No.2013BAD17B06)
文摘The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.
基金the National Natural Science Foundation of China(10301033 and 10271113)
文摘This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
文摘In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.