A SURVEY ON χ-MODULE CONNES AMENABILITY OF SEMIGROUP ALGEBRAS

We shall study the χ-module Connes amenability of a semigroup algebra l^۱(S),where χ is a bounded module homomorphism from l^۱(S) to l^۱(S) that is w^∗-continuous and S is an inverse weakly cancellative semigroup with subsemigroup E of idempotents. We are mainly concerned with the study of χ-module normal, virtual diagonals. We characterize the χ- module Connes amenability of a semigroup algebra l^۱(S). Also, we show that if l^۱(S) as a Banach module over l^۱(E) has an id-module normal, virtual diagonal then it is id-module Connes amenable. Other characterizations of χ- module Connes amenability of l^۱(S) is presented.

کلیدواژه ها:

χ-module Connes amenable ، module χ-derivation ، χ-module normal virtual diagonal ، weakly cancellative semigroup