Permanence properties for crossed products and fixed point algebras of finite groups
Permanence properties for crossed products and fixed point algebras of finite groups
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有限群的交叉积和不动点代数的持久性
DOI：
10.1090/s0002-9947-2014-06036-4
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发表时间：
2012
影响因子：
1.3
通讯作者：
N. Phillips
中科院分区：
文献类型：
--
作者：
C. Pasnicu;N. Phillips
对于有限群在C*-代数上的作用，给出了C*-代数的性质传递到交叉积或不动点代数的条件.我们主要考虑理想性质、投影性质、拓扑维数零和纯无限性。在我们的许多结果中，附加的条件对群、代数或作用是必要的。有时作用必须是强逐点外的，在一些结果中它必须具有Rokhlin性质。当群是有限交换群时，我们证明了交叉积和不动点代数保持拓扑维数为零，而不需要对作用作任何条件。
我们给出一个例子来说明理想性质和投影性质不传递到不动点代数（即使是二元群）。该构造还给出了一个C*-代数的例子，它不具有理想性质，但使得它上的2 × 2矩阵代数具有理想性质;事实上，这个矩阵代数具有投影性质。
For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property, topological dimension zero, and pure infiniteness. In many of our results, additional conditions are necessary on the group, the algebra, or the action. Sometimes the action must be strongly pointwise outer, and in a few results it must have the Rokhlin property. When the group is finite abelian, we prove that crossed products and fixed point algebras preserve topological dimension zero with no condition on the action.
We give an example to show that the ideal property and the projection property do not pass to fixed point algebras (even for the two element group). The construction also gives an example of a C*-algebra which does not have the ideal property but such that the algebra of 2 by 2 matrices over it does have the ideal property; in fact, this matrix algebra has the projection property.
影响因子：
2.5
作者：
Masaki Izumi
通讯作者：
Masaki Izumi