Tabular algebras and their asymptotic versions

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.