The Topology on the Primitive Ideal Space of Transformation Group C # - Algebras and C.C.R. Transformation Group C # -Algebras
The Topology on the Primitive Ideal Space of Transformation Group C # - Algebras and C.C.R. Transformation Group C # -Algebras
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变换群C的本原理想空间拓扑
DOI：
10.1090/s0002-9947-1981-0617538-7
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
Dana P. Williams
中科院分区：
文献类型：
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作者：
Dana P. Williams
如果(G，8)是第二可数变换群，且稳定群是服从的，则C*(G，8)是C.C.R.当且仅当轨道是闭的，且稳定群是C.C.R.此外，在不可分的情况下得到了闭轨与C.C.R.代数有关的部分结果。在某些情况下，本原理想空间的拓扑是显式计算的。特别地，如果稳定群都包含在一个固定的交换子群H中，则根据H和轨道结构计算拓扑，只要C*(G，8)和C*(H，8)是EH-正则的。如果G是交换的且(G，8)是第二可数的，则这些条件自动满足。
If (G, 8) is a second countable transformation group and the stability groups are amenable then C*(G, 8) is C.C.R. if and only if the orbits are closed and the stability groups are C.C.R. In addition, partial results relating closed orbits to C.C.R. algebras are obtained in the nonseparable case. In several cases, the topology of the primitive ideal space is calculated explicitly. In particular, if the stability groups are all contained in a fixed abelian subgroup H, then the topology is computed in terms of H and the orbit structure, provided C*(G, 8) and C*(H, 8) are EH-regular. These conditions are automatically met if G is abelian and (G, 8) is second countable.