Morita Equivalence of Brandt Semigroup Algebras

Abstract

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 $H^n(\ell (B(I,G)),E^{\ast })$ are trivial, and also, the notion of approximate amenability is not Morita invariant.

arXiv comment9 Pages

References in corpus (1)

• Pseudo-amenability of Brandt semigroup algebras