Morita Equivalence of Brandt Semigroup Algebras

Details Morita Equivalence of Brandt Semigroup Algebras Morita Equivalence of Brandt Semigroup Algebras

2008-08-21

arxiv.org/abs/0808.2942v1

Mathematics

Functional Analysis

9 Pages

Scientific paper

We prove that for every group $G$ and any two sets $I,J$, the Brandt semigroup algebras $\ell(B(I,G))$ and $\ell(B(J,G))$ 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 $\ell(B(I,G))$-bimodules $E$, and every $n>0$, the bounded Hochschild cohomology groups $H^n(\ell(B(I,G)),E^*)$ are trivial, and also, the notion of approximate amenability is not Morita invariant.

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