Morita Equivalence of Brandt Semigroup Algebras

2008/08/21 by Maysam Maysami Sadr, Sadr, Maysam Maysami
Mathematics · #16D90 #16E40 #20M25 #46H05 #46H25 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0808.2942

openalex publication_date 2008/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every group G and any two sets I,J, the Brandt semigroup algebras ℓ(B(I,G)) and ℓ(B(J,G)) are Morita equivalent with respect to the Morita theory of self-induced Banach algebras introduced by Gronbaek. As applications, we show that if G is an amenable group, then for a wide class of Banach ℓ(B(I,G))-bimodules E, and every n>0, the bounded Hochschild cohomology groups Hⁿ(ℓ(B(I,G)),E^*) are trivial, and also, the notion of approximate amenability is not Morita invariant.

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