On contractibility of the Gelfand spectrum of semigroup measure algebras

TL;DR

This paper investigates conditions under which the Gelfand spectrum of semigroup measure algebras is contractible, providing both sufficient and necessary conditions for a broad class of semigroups.

Contribution

It offers new criteria for contractibility of the Gelfand spectrum and establishes their necessity for many semigroups, advancing understanding in harmonic analysis.

Findings

Provided sufficient conditions for contractibility.

Showed these conditions are necessary for a wide class of semigroups.

Enhanced understanding of the structure of semigroup measure algebras.

Abstract

Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.