Tabular algebras and their asymptotic versions

TL;DR

This paper introduces tabular algebras, generalizing cellular and table algebras, and explores their asymptotic versions, providing explicit structural descriptions and examining natural examples.

Contribution

It defines tabular algebras, establishes conditions for their asymptotic versions, and analyzes key examples, advancing the understanding of algebraic structures in this area.

Findings

Existence of asymptotic versions under trace conditions

Explicit structure determination of asymptotic algebras

Analysis of natural examples of tabular algebras

Abstract

We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of trace map then the algebra has a corresponding asymptotic version whose structure can be explicitly determined. We also study various natural examples of tabular algebras.