具有Cuntz半群消去律的C^(*)-代数  

C^(*)-algebras of Cuntz semigroups with cancellation properties

作　　者：范庆斋[1] 安璐 FAN Qingzhai;AN Lu(College of Arts&Sciences,Shanghai Maritime University,Shanghai 201306,China)

机构地区：[1]上海海事大学文理学院,上海201306

出　　处：《上海海事大学学报》2022年第4期120-124,共5页Journal of Shanghai Maritime University

基　　金：国家自然科学基金(11501357)。

摘　　要：设Ω是一类具有Cuntz半群弱消去律(或者具有Cuntz半群投影消去律)的C^(*)-代数。证明Cuntz半群的弱消去律(或者Cuntz半群的投影消去律)可以遗传到由Ω中C^(*)-代数迹逼近后得到的C^(*)-代数类中。作为上述结论的应用:若A是一个无限维有单位元单的具有弱消去律(或者具有投影消去律)性质的C^(*)-代数,且设α:G→Aut(A)是有限群G作用在A上并且作用具有迹Rokhlin性质,则交叉积C^(*)-代数C^(*)(G,A,α)的Cuntz半群具有弱消去律(或者具有投影消去律)。LetΩbe a class of C^(*)-algebras of Cuntz semigroups with the weakly cancellation property(or with the projection cancellation property).It is proved that the weakly cancellation property(or the projection cancellation property)of Cuntz semigroups can be inherited to the C^(*)-algebra class obtained by the C^(*)-algebra tracial approximation inΩ.It is applied as follows:if A be an infinite-dimensional unital simple C^(*)-algebra such that A has the weakly cancellation property(or has the projection cancellation property),and suppose thatα:G→Aut(A)is an action of a finite group G on A which has the tracial Rokhlin property,then the Cuntz semigroup of the crossed product C^(*)-algebra C^(*)(G,A,α)also has the weakly cancellation property(or the projection cancellation property).

关 键 词：C^(*)-代数 迹逼近 Cuntz半群 

分 类 号：O177[理学—数学]