Tabular algebras and their asymptotic versions.

Green, Richard (2002) Tabular algebras and their asymptotic versions. Journal of Algebra, 252 (1). pp. 27-64. ISSN 0021-8693

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.