A SURVEY ON χ-MODULE CONNES AMENABILITY OF SEMIGROUP ALGEBRAS

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Document Type : Original Manuscript

Authors

1 Department of Mathematics, Velayat University, P.O. Box 9917638733, Iranshahr, Iran.

2 Department of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan, Iran.

Abstract

We shall study the χ-module Connes amenability of a semigroup algebra l^1(S),where χ is a bounded module homomorphism from l^1(S) to l^1(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^1(S). Also, we show that if l^1(S) as a Banach module over l^1(E) has an id-module normal, virtual diagonal then it is id-module Connes amenable. Other characterizations of χ- module Connes amenability of l^1(S) is presented.

Keywords

References

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Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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