拟对角扩张C~*-代数Cuntz半群的性质  

Cuntz semigroup properties of quasidiagonal extension C~*-algebras

作　　者：方燕[1] FANG Yan(School 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》2018年第4期106-108,共3页Journal of Shanghai Maritime University

基　　金：国家自然科学基金(11501357)

摘　　要：设0→I→B→πA→0是一个拟对角扩张。为研究C*-代数B的性质,对C*-代数B的理想I和商代数A的性质进行研究。证明如下结论:(1)如果I和A具有无孔性质,则B也具有无孔性质;(2)如果I和A具有弱可分性质,则B也具有弱可分性质;(3)如果I和A具有Riesz插值性质,则B也具有Riesz插值性质。上述结论可以用来研究非单的C*-代数的正则性质。Let0→I→B→πA→0be a quasidiagonal extension.To study the properties of C*-algebra B,the properties of the ideal I and the quotient algebra A of C*-algebra B are studied.The following conclusions are proved:(1)suppose that I and A have the unperforated property,then B has the unperfoarated property;(2)suppose that I and A have the weakly separative property,then B has the weakly separative property;(3)suppose that I and A have the Riesz interpolation property,then B has the Riesz interpolation property.The conclusions can be used to study the regular property of non-simple C*-algebras.

关 键 词：C*-代数 拟对角扩张 Cuntz半群 

分 类 号：O177[理学—数学]