Cohomology groups of a new class of Kadison-Singer algebras

作     者：Guangyu An Xing Cheng Jun Sheng 

作者机构：School of Mathematics and Data ScienceShaanxi University of Science and TechnologyXi’an 710021China 

出 版 物：《Science China Mathematics》 (中国科学（数学）（英文版）)

年 卷 期：2024年第67卷第3期

页      面：593-606页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11801342) Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043) Shaanxi College Students Innovation and Entrepreneurship Training Program(Grant No.S202110708069) 

主　　题：Kadison-Singer algebra Kadison-Singer lattice derivation cohomology group 

摘      要：Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N ,E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and *** show that L is a Kadison-Singer lattice with the trivial ***,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.