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
We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an ap...We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.展开更多
Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant s...Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞).展开更多
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irration...Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr（Aω） = tr（Aρ）. It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω. has a group structure, denoted by π1（Aut（Aω.））, which is isomorphic to Z if d > 1 and {0} if d > 1. Let Bcd be a cd-homogeneous C*-algebra over S2 x T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torns Sρcd is defined by twisting C*（T2 x Zm-2） in Bcd C* （Z（m-2）） by a totally skew multiplier ρ on T2 x Z（m-2）. It is shown that Sρcd Mp∞ is isomorphic to C（S2） C* （T2 x Zm-2, ρ） Mcd（C） Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.展开更多
The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are...The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.展开更多
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irration...Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr（Aω） = tr（Aρ）. It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω. has a group structure, denoted by π1（Aut（Aω.））, which is isomorphic to Z if d 】 1 and {0} if d 】 1. Let B<sub>cd</sub> be a cd-homogeneous C*-algebra over S2 x T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torns S<sub>ρ</sub><sup>cd</sup> is defined by twisting C*（T2 x Zm-2） in B<sub>cd</sub> C* （Z（m-2）） by a totally skew multiplier ρ on T2 x Z（m-2）. It is shown that Sρcd Mp∞ is isomorphic to C（S2） C* （T2 x Zm-2, ρ） Mcd（C） Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.展开更多
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 National Natural Sciences Foundation of China(Grant Nos.11501357 and 11571008)。
文摘We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.
文摘Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞).
基金Project supported by the grant No. 1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF
文摘Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr（Aω） = tr（Aρ）. It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω. has a group structure, denoted by π1（Aut（Aω.））, which is isomorphic to Z if d > 1 and {0} if d > 1. Let Bcd be a cd-homogeneous C*-algebra over S2 x T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torns Sρcd is defined by twisting C*（T2 x Zm-2） in Bcd C* （Z（m-2）） by a totally skew multiplier ρ on T2 x Z（m-2）. It is shown that Sρcd Mp∞ is isomorphic to C（S2） C* （T2 x Zm-2, ρ） Mcd（C） Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.
基金Project supported by Grant No.1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF.
文摘The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.
基金Project supported by the grant No. 1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF
文摘Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aω of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr（Aω） = tr（Aρ）. It is proved that the set of all C*-algebras of sections of locally trivial C*-algebra bundles over S2 with fibres Aω. has a group structure, denoted by π1（Aut（Aω.））, which is isomorphic to Z if d 】 1 and {0} if d 】 1. Let B<sub>cd</sub> be a cd-homogeneous C*-algebra over S2 x T2 of which no non-trivial matrix algebra can be factored out. The spherical noncommutative torns S<sub>ρ</sub><sup>cd</sup> is defined by twisting C*（T2 x Zm-2） in B<sub>cd</sub> C* （Z（m-2）） by a totally skew multiplier ρ on T2 x Z（m-2）. It is shown that Sρcd Mp∞ is isomorphic to C（S2） C* （T2 x Zm-2, ρ） Mcd（C） Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.
