Fixed point algebras for weakly proper Fell bundles

2020/09/02 by Damián Ferraro, Ferraro, Damián
Mathematics · Medicine · #46L55 (Primary) #46L99 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Neurological and metabolic disorders #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2009.01071

openalex publication_date 2020/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define weakly proper Fell bundles and construct exotic fixed point algebras for such bundles. Three alternative constructions of such algebras are given. Under a kind of freeness condition, one of our constructions implies that every exotic cross sectional C*-algebra of a weakly proper Fell bundle is Morita equivalent to an exotic fixed point algebras. The other constructions are used to show that ours generalizes that of Buss and Echterhoff on weakly proper actions on C*-algebras. We also generalize to Fell bundles the fact that every C*-action which is proper in Kasparov's sense is amenable.

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