Module cohomological properties of the Fourier algebra of an inverse semigroup

TL;DR

This paper investigates the module cohomological properties of the Fourier algebra associated with an inverse semigroup, establishing conditions for various forms of module amenability and biflatness.

Contribution

It provides necessary and sufficient conditions for the Fourier algebra of an inverse semigroup to have specific module cohomological properties.

Findings

Conditions for module amenability of A(S)

Conditions for module character amenability

Conditions for module biflatness and biprojectivity

Abstract

For an inverse semigroup S with the set of idempotents E and a minimal idempotent, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat, or module (operator) biprojective.