Transformation group C1-algebras with continuous trace |
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Authors: | Dana P Williams |
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Affiliation: | Department of Mathematics, Texas A & M University, College Station, Texas 77843 U.S.A. |
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Abstract: | We obtain several results characterizing when transformation group C1-algebras have continuous trace. These results can be stated most succinctly when () is second countable, and the stability groups are contained in a fixed abelian subgroup. In this case, has continuous trace if and only if the stability groups vary continuously on Ω and compact subsets of Ω are wandering in an appropriate sense. In general, we must assume that the stability groups vary continuously, and if () is not second countable, that the natural maps of onto G · x are homeomorphisms for each x. Then has continuous trace if and only if compact subsets of Ω are wandering and an additional C1-algebra, constructed from the stability groups and Ω, has continuous trace. |
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