Pseudo-contractibility and pseudo-amenability of semigroup algebras

摘要

In this paper, we characterize pseudo-contractibility of ?~1(S), where S is a uniformly locally finite inverse semigroup. As a consequence, we show that for a Brandt semigroup S=M~o(G,I),the semigroup algebra ?~1(S) is pseudo-contractible if and only if G and I are finite. Moreover, we study the notions of pseudo-amenability and pseudo-contractibility of a semigroup algebra ?~1(S) in terms of the amenability of S.