Strongly self-absorbing property for inclusions of C*-algebras with a finite Watatani index
Strongly self-absorbing property for inclusions of C*-algebras with a finite Watatani index
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具有有限 Watatani 指数的 C* 代数包含体的强自吸收特性
DOI：
10.1090/s0002-9947-2013-05907-7
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Teruya
中科院分区：
文献类型：
--
作者：
H. Osaka;T. Teruya
设是单位代数的包含，是指数有限型的条件期望。引入了一个Rokhlin性质，讨论了-吸收性质，其中是一个可分的、有单位元的、强自吸收代数，即，，存在一个同构，使得它近似酉等价于嵌入。无限型UHF代数、Jiang-Su代数和Cuntz代数都是强自吸收代数的典型例子。本文研究了具有有限Watatani指标的单位代数包含下强自吸收的持久性。我们显示以下内容：
Letbe an inclusion of unital-algebras andbe a conditional expectation of index-finite type. We introduce a Rokhlin property forand discuss the-absorbing property, whereis a separable, unital, strongly self-absorbing-algebra, ie,, and there exists an isomorphismsuch thatis approximately unitarily equivalent to the embedding. UHF algebras of infinite type, the Jiang–Su algebra, and Cuntz algebrasandare typical examples of strongly self-absorbing-algebras. In this paper, we consider permanence properties for a strongly self-absorbing property under inclusions of unital-algebras with a finite Watatani index. We show the following: