Cellularity of diagram algebras as twisted semigroup algebras

TL;DR

This paper establishes a general theorem proving the cellularity of twisted semigroup algebras of regular semigroups, unifying and extending previous results on diagram algebras like Temperley-Lieb, Brauer, and partition algebras.

Contribution

It introduces a broad theorem that confirms the cellularity of twisted semigroup algebras, generalizing prior specific cases to a wider class of algebras.

Findings

Proves cellularity for a wide class of twisted semigroup algebras

Unifies previous results on Temperley-Lieb, Brauer, and partition algebras

Simplifies the verification of cellularity in these algebras

Abstract

The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups. This theorem, which generalises a recent result of East about semigroup algebras of inverse semigroups, allows us to easily reproduce the cellularity of these algebras.