自反算子代数的模和交换子以及一阶上同调空间  

Modules and Commutants and First Cohomology Spaces of Reflexive Algebras

作　　者：陈培鑫[1] 鲁世杰[2] 

机构地区：[1]南京理工大学数学系,南京210094 [2]浙江大学数学系(城市学院),杭州310027

出　　处：《数学学报（中文版）》2003年第5期875-882,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H^1(AlgL,B(H))=0的一阶上同调空间H^1(AlgL,M)被刻划。Let (?) be a subspace lattice on a normed linear space. The necessary and sufficient conditions for a subspace to be a reflexive Alg?module are obtained. Suppose ?is a completely distributive subspace lattice, M is an arbitrary reflexive Alg(?)-module. The double commutant of M is the described. Furthermore, a class of lattices called V-generators dense lattices is introduced, which strictly includes the class of completely distributive lattices and the class of pentagon lattices. Let ?be a V-generators dense and commutative subspace lattice (GDCSL for short), M be any reflexive Alg(?)-module. The commutant C(Alg(?),.M) of Alg?modulo M and the algebra AlgLat.M are all decomposed as direct sums. A description for the first cohomology H1(Alg(?), M) with H1(Alg(?),B(H)=0 is given.

关 键 词：模模交换子 ∨-生成子稠格 一阶上同调空间 

分 类 号：O177.1[理学—数学]