The linear span of projections in AH algebras and for inclusions of C*-algebras
The linear span of projections in AH algebras and for inclusions of C*-algebras
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AH 代数和 C* 代数包含的投影的线性跨度
DOI：
10.1155/2013/204319
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发表时间：
2013
影响因子：
--
通讯作者：
H. Osaka
中科院分区：
文献类型：
--
作者：
D. T. Hoa;T. M. Ho;H. Osaka
本文的第一部分证明了AH代数具有LP性质当且仅当Ai的中心的每个元素都属于A中投影的线性跨度的闭包。因此，对角AH-代数具有LP性质，如果它在Bratteli和Elliott意义下具有小的特征值变化。本文的第二个贡献是，对于包含具有有限Watatani指标的酉C *-代数P → A，如果忠实条件期望E：A→ P具有Kodaka等人意义下的Rokhlin性质，则在A具有LP性质的条件下，P具有LP性质。作为应用，设Abe是具有LP性质的单酉C *-代数，α是有限群Gonto Aut（A）的作用.若α具有Izumi意义下的Rokhlin性质，则不动点代数AG和交叉积代数A <$α G具有LP性质.我们还指出，CAR代数上存在一个对称性，使得它的不动点代数不具有LP性质。
In the first part of this paper, we show that an AH algebrahas the LP property if and only if every element of the centre ofAibelongs to the closure of the linear span of projections inA. As a consequence, a diagonal AH‐algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unitalC*‐algebrasP⊂Awith a finite Watatani index, if a faithful conditional expectationE:A→Phas the Rokhlin property in the sense of Kodaka et al., thenPhas the LP property under the condition thatAhas the LP property. As an application, letAbe a simple unitalC*‐algebra with the LP property,αan action of a finite groupGonto Aut(A). Ifαhas the Rokhlin property in the sense of Izumi, then the fixed point algebraAGand the crossed product algebraA⋊αGhave the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.