2000/12/12 by Ruy Exel, Exel, Ruy · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA
paper · pdf · doi:10.48550/arxiv.math/0012091
8 pages, Plain TeX
arxiv created 2000/12/12 · arxiv updated 2009/11/30
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.