Exact Groups, Induced Ideals, and Fell Bundles

Details Exact Groups, Induced Ideals, and Fell Bundles Exact Groups, Induced Ideals, and Fell Bundles

2000-12-12

arxiv.org/abs/math/0012091v1

Mathematics

Operator Algebras

8 pages, Plain TeX

Scientific paper

Given a C*-algebra B which is graded over a discrete group G we consider ideals of B which are invariant under the projections onto each of the grading subspaces. If G is exact and the standard conditional expectation of B is faithful we show that all such ideals are induced, i.e. are generated by their intersection with the unit fiber algebra. This result is derived from a generalization to the context of Fell bundles of a Theorem by Kirchberg and Wasserman according to which a group is exact if and only if its reduced C*-algebra is exact.

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