C(X)A上的自同构群

本文研究了连续函数代数C（X）与某个C*-代数A的张量积C（X）A的自同构群．当A是有单位元且具有平凡中心的C*-代数时,本文完全刻划了C（X）A的自同构群．利用AF-代数的K-理论,本文还刻划了当X是全不连通的紧致Hausdorff空间时,C（X）与紧算子理想的张量积的自同构群．     

The automorphism group of the Toeplitz algebra onH2(T2)

The automorphism group of the C^* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .     

The automorphism group of the Toeplitz algebra onH 2(T2)

The automorphism group of the C^* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .     

C(X) A上的自同构群

本文研究了连续函数代数C(X)与某个C*-代数 A的张量积C(X) A的自同构群.当 A是有单位元且具有平凡中心的C*-代数时,本文完全刻划了C(X) A的自同构群.利用AF-代数的K-理论,本文还刻划了当X是全不连通的紧致Hausdorff空间时,C(X)与紧算子理想的张量积的自同构群.     

Toeplitz Algebras on Dirichlet Spaces

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＢｎｂｅｔｈｅｕｎｉｔｂａｌｌｉｎＣｎ,ａｎｄｄｖｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＢｎ.ＳｏｂｏｌｅｖｓｐａｃｅＬ2 ,1ｉｓｔｈｅｓｐａｃｅｏｆｆｕｎｃｔｉｏｎｓｕ :Ｂｎ→Ｃ ,ｆｏｒｗｈｉｃｈｔｈｅｎｏｒｍ‖ｕ‖1/ 2 =∑ｎｉ=1 ∫Ｂｎ ｕ ｚｉ(ｚ) 2 + ｕ ｚｉ(ｚ) 2 ｄν1/ 2 <∞ .Ｌ2 ,1/ 2 ｉｓａＨｉｌｂｅｒｔｓｐａｃｅｗｉｔｈｔｈｅｉｎｎｅｒｐｒｏｄｕｃｔ〈ｕ ,ｖ〉1/ 2 =∑ｎｉ=1〈 ｕ ｚｉ, ｕ ｚｉ〉Ｌ2 (ｄν) +∑ｎｉ=1〈 ｕ ｚｉ, ｕ …     

C~*标准代数中效应的序列同构

主要借助于C~*标准算子代数中的有限秩算子对一般的效应元进行刻画.证明了C~*标准算子代数A的效应代数E(A)上的每个序列自同构和自同构ψ都具有形式ψ(A)=UAU~*,其中A∈E(A),U为酉算子或反酉算子.     

Derivations on LMC*-Algebras

It is shown that derivations on LMC*-algebras are always continuous and generate a continuous one-parameter group of automorphisms. The structure of the derivation and the automorphism group on LMC*-algebras is investigated.     

Compact quantum group actions on C*-algebras and invariant derivations

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

     

一类Smale空间上的C~*-代数自同构的熵

Ian Putnam利用Smale空间上的渐近等价关系定义了广群C~*-代数及其典则自同构.本文在零维Smale空间的情形下,计算此类C~*-自同构的逼近熵,证明了相应C~*-动力系统关于CNT熵和逼近熵的"变分原理"成立.由此推演出此类Smale空间上的Bowen测度诱导的C~*-代数上的态是此典则自同构的唯一平衡态.     

TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

The automorphism group of the Toeplitz C-algebra,J(C~1),generated by Toeplitz op-erators with C~1-symbols on Dirichlet space D is discussed;the K_0,X_1-groups and the firstcohomology group of J(C~1)are computed.In addition,the author provs that the spectraof Toeplitz operators with C~1-symbols are always connected,and discusses the algebraic prop-erties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjointToeplitz operator on D and T_φ~*=T_φ if and only if T_φ is a scalar operator.     

一类基于量子环面非交换结合代数的模

在量子环面[1]上构造一类非交换结合代数AQ-模M(a,b),我们还刻划了AQ-模的结构并揭示[2]一类商模序列:每个商模Mn(a)/Mn+1(a)都同构于M(a,0),每个商模的自同构群AutMn(a)/Mn+1(a)均与C*同构.     

有限生成自由代数FV（LK）（n）的自同构群（英文）

本文研究了自同构群AutLk和AutFV(LK)(n)的结构问题.利用了正交模格及其自同构群的直积分解方法,获得了正交模格Lk和自由代数FV(LK)(n)的自同构群的直积分解式.     

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G.     

The group of holomorphic automorphisms in certainJ *-Algebras

Summary The group of all holomorphic automorphisms of the infinite-dimensional analogue of the Cartan domain of type I is determined, by the characterisation of all surjective linear isometries ofL(K, H) (K, H Hilbert spaces). Also a linear representation of the group is given, and the study of the fixed points set for a holomorphic automorphism of the unit ball of a J*-algebra.Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

2-Local Automorphisms on Basic Classical Lie Superalgebras

Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).     

2-Local automorphisms of operator algebras

A not necessarily continuous, linear or multiplicative function θ from an algebra A into itself is called a 2-local automorphism if θ agrees with an automorphism of A at each pair of points in A. In this paper, we study when a 2-local automorphism of a C^∗-algebra, or a standard operator algebra on a locally convex space, is an automorphism.     

非拟本原（PSU3（P），2）-弧传递图的外自同构

证明由GF（p^2）的域自同构可以产生一类非拟本原（PSU3（P），2）-弧传递图的白同构，并研究了这样的自同构与图的传递自同构群中心化予的关系。     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

An automorphism of the geometry of the group B2(2n) as a polynomial map

A construction of an automorphism of the geometry of the group B₂(2ⁿ) is given as an extension of an automorphism of a root system. Some properties of the automorphism are proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1530–1534, November, 1992.     

拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.