Twisted bounded-dilation group C*-algebras as C*-metric algebras  

作　　者：Botao Long Wei Wu 

机构地区：[1]Research Center for Operator Algebras,East China Normal University,Shanghai 200241,China [2]School of Mathematical Sciences,Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,East China Normal University,Shanghai 200241,China

出　　处：《Science China Mathematics》2021年第3期547-572,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171109 and 11801177);the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。

摘　　要：We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.

关 键 词：discrete group boundedθ-dilation twisted reduced group C*-algebra C*-metric algebra Leibniz Lip-norm compact quantum metric space 

分 类 号：O15[理学—数学]