Simplicity of contracted inverse semigroup algebras

Abstract: If $S$ is an inverse semigroup with a zero element, the contracted semigroup algebra $K_0S$ is obtained from the semigroup algebra by identifying the zero of $S$ with the zero of the field. In the talk, we examine when $K_0S$ is simple. It is easy to see that $S$ congruence-free is a necessary condition, as non-trivial congruences of $S$ give rise to non-trivial ideals of $K_0S$. It has been known for long that this condition is not sufficient however. Munn in the late 70's asked to characterize when a congruence-free inverse semigroup with zero has a simple contracted semigroup algebra. A partial answer was given by Steinberg in 2016, under the additional assumption that the inverse semigroup is Hausdorff. In the talk, we present a complete answer to Munn's question.

category theorygroup theoryrings and algebras

Audience: researchers in the topic

York semigroup seminar

Series comments: Description: Semigroup-related research talks at University of York.

Email Nora Szakacs at nora.szakacs@york.ac.uk for the meeting password.