Dilations and full corners on fractional skew monoid rings

TL;DR

This paper extends the dilation results for fractional skew monoid rings with cancellative left Ore monoids acting via corner isomorphisms to more general settings and explores applications to semigroup C*-crossed products.

Contribution

It generalizes the dilation theorem for fractional skew monoid rings beyond previous restrictions and applies it to semigroup C*-crossed products.

Findings

Dilation result holds in full generality for fractional skew monoid rings.

Application of the dilation result to semigroup C*-crossed products.

Enhanced understanding of the structure of fractional skew monoid rings.

Abstract

In this note we will show that the dilation result obtained for fractional skew monoid rings, in the case of a cancellative left Ore monoid $S$ acting on a unital ring $A$ by corner isomorphisms, holds in full generality. We apply this result to the context of semigroup $C^*$-crossed products.