THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS

Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ）× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p.     

LENTICULAR NONCOMMUTATIVE TORI

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     

量子环面上一类导子李代数的结构和自同构群

本文研究量子环面上的一类导子李代数,它包含了Virasoro-Like代数及其q类似.首先证明了这类导子李代数之间的同构一定是分次同构,并进一步给出了代数同构的充要条件及同构映射的具体表达式,最后确定了该类李代数的自同构群.     

量子环面上一类导子李代数的结构和自同构群

本文研究量子环面上的一类导子李代数,它包含了Virasoro-Like代数及其q类似．首先证明了这 类导子李代数之间的同构一定是分次同构,并进一步给出了代数同构的充要条件及同构映射的具体表达 式,最后确定了该类李代数的自同构群．     

Smale空间上的广群C~*-代数的迹

本文证明由拓扑混合的Smale空间上的渐进等价关系定义的广群C*-代数及其相应的Ruelle代数有唯一的迹态;在拓扑可迁的情形下,证明此C*-代数的迹态构成了一个单形,此单形顶点的个数等于“Smale谱分解”中基本空间的个数,单形的重心是该C*-代数的唯一的αa-不变迹态;此回答了I.Putnam的一个猜测.     

NEW OBSTRUCTIONS FOR THE SURJECTIVITY OF THE JOHNSON HOMOMORPHISM OF THE AUTOMORPHISM GROUP OF A FREE GROUP

In this paper we construct new obstructions for the surjectivityof the Johnson homomorphism of the automorphism group of a freegroup. We also determine the structure of the cokernel of theJohnson homomorphism for degrees 2 and 3.     

THE HOLOMORPHIC AUTOMORPHISM GROUP OF HIGHER DIMENSION THULLEN DOMAIN

In this paper, we give the holomorphic automorphism group of the higher-dimensional generalization of Thullen domain.     

GENERALIZATION OF THE NOTION OF FUNDAMENTAL GROUP

The classical definition of fundamental group for a topological space is based on the pathwise connectedness. A space with less path will not be able to be described effectively by its fundamental group. The author introduces a definition of generalized fundamental group for a given topological space by means of its own connectedness. For a well-behaved space, e.g., a locally pathwise and semilocally simply connected compact metric space, the generalized fundamental group coincides with the classical one.     

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献   

有限群的Coleman外自同构群是p''-群的一些充分条件

本文研究了有限群G的Coleman外自同构群是p'-群这个问题. 利用Sylow p-子群和同调群的性质,得到了有限群的Coleman外自同构群是p'-群的一些充分条件,其结果与M.Hertweck和W.Kimmerle得到的结果是不同的.     

Quasidiagonal representations of nilpotent groups

We show that every unitary representation of a discrete solvable virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G   approximately decomposes as a direct sum of finite dimensional approximate representations. In operator algebraic terms we show that C^?(G)$C^{?}(G)$ is strongly quasidiagonal.     

THE FUNDAMENTAL GROUP IN FIBRATIONS

A generalized Mayer-Vietoris sequence involving crossed homomorphisms is established and the construction is applied to the homotopy sequence of the CW-pair (X.X¹) to relate the homotopy sequences of (X.X¹) and the fibre bundle F → E → X in low dimensions. If there is a partial cross-section of E → X over X², the classical form, π₁ E ～ π₁ [xtilde] π₁ F as a semidirect product, results. In case there is no extension over X² of any cross-section of the restricted bundle χ:π₂ (x², x¹) → X¹ the corresponding obstruction map X_E:π₂(x²,x¹) → π₁F is non-trivial and in case F → E → X is an SO(n)-bundle (n ≥ 3), χ_E maps into a subgroup of the centre, Z(π₁ F), of order at most 2.     

关于Gelfand-Mazur型的两个定理

证明了两个Gelfand-Mazur型的定理，其一是：设A是一单位C^*- wa ovt ,AH≌R，且h∈AK时，e^h具有凸谱集。则A≌C。这一结果回答了Bhatt等人的问题，给出了他们的结果在实情形中的结论。其二，部分地回答了Bhatt等人的另一个问题。结果是：设A是一复单位厄米Banach^*- 代数，假设（i)对任意x∈AH，谱集σA(x)的内部是空集，且C\σA（x)是连通的，（ii)A没有非零零因子，则A同构到C。     

A Perturbation of Jensen *-Derivations from K(H) into K(H)

Let's take H as an infinite–dimensional Hilbert space and K( H) be the set of all compact operators on H. Using Spectral theorem for compact self–adjoint operators, we prove the Hyers–Ulam stability of Jensen *-derivations from K( H) into K( H).     

A Longitudinal Lefschetz Theorem in K-Theory

We give a leafwise Lefschetz theorem in the localized equivariant K-theory of a compact foliated manifold. The method is a generalization of the one adopted by M.F. Atiyah and G. Segal in the nonfoliated case. The main tool is the equivariant version of the Connes–Skandalis longitudinal index theorem for foliations. As a byproduct, we obtain a generalization of the Heitsch–Lazarov measured Lefschetz formula to arbitrary complexes with the explicit formula for the integrand, when the diffeomorphism belongs to a compact Lie group acting on the compact manifold.     

一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

ON THE SHEAF OF GENERALIZED FUNDAMENTAL GROUP AND COVERING SPACE

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The stable rank of full corners in C*-algebras

We give a treatment of Rieffel's theory of stable rank for C*-algebras in terms of left invertibility of generalized nonsquare matrices, and prove that if is a full projection in a unital C*-algebra , then the stable rank of the corner is at least as large as the stable rank of .