Connective C*-Algebras
Connective C*-Algebras
复制标题
联结 C*-代数
DOI：
10.1016/j.jfa.2017.02.009
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
U. Pennig
中科院分区：
文献类型：
--
作者：
M. Dadarlat;U. Pennig
连通性是可分C-代数的同伦不变性质，它有三个显著的结果：不存在非平凡投影，拟对角性和使用渐近态射对核C-代数的KK-理论的几何实现。本文的目的是进一步探讨连通C-代数类。给出了正合和核可分C <$-代数的连通性的新刻画，证明了连通可分核C <$-代数的扩张是连通的。我们建立了连通性或缺乏连通性的C-代数相关联的某些类的群体：虚拟交换群，线性连通幂零李群和线性连通半单李群。
Connectivity is a homotopy invariant property of separable C⁎-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C⁎-algebras using asymptotic morphisms. The purpose of this paper is to further explore the class of connective C⁎-algebras. We give new characterizations of connectivity for exact and for nuclear separable C⁎-algebras and show that an extension of connective separable nuclear C⁎-algebras is connective. We establish connectivity or lack of connectivity for C⁎-algebras associated to certain classes of groups: virtually abelian groups, linear connected nilpotent Lie groups and linear connected semisimple Lie groups.