Pseudo-amenability and pseudo-contractibility of restricted semigroup algebra

Abstract

In this article the pseudo-amenability and pseudo-contractibility of restricted semigroup algebra lr1(S) and semigroup algebra, l1(Sr) on restricted semigroup, Sr are investigated for different classes of inverse semigroups such as Brandt semigroup, and Clifford semigroup. We particularly show the equivalence between pseudo-amenability and character amenability of restricted semigroup algebra on a Clifford semigroup and semigroup algebra on a restricted semigroup. Moreover, we show that when S=M0(G,I) is a Brandt semigroup, pseudo-amenability of l1(Sr) is equivalent to its pseudo-contractibility.

Keywords

• pseudo-amenable
• pseudo-contractible
• restricted semigroup
• semigroup algebra.