Johnson pseudo-contractibility of certain semigroup algebras

Abstract

In this paper we characterize the Johnson pseudo-contractibility of \(\ell ^{1}(S)\), where S is a uniformly locally finite inverse semigroup. We show that for a Brandt semigroup \(S=M^{0}(G,I)\) over a non-empty set I, \(\ell ^{1}(S)\) is Johnson pseudo-contractible if and only if G is amenable and I is finite. We give some examples to show the difference between Johnson pseudo-contractibility, pseudo-amenability and pseudo-contractibility among the semigroup algebras.