Common properties of table algebras and association schemes

A. Rahnamai Barghi
2008 Discrete Mathematics  
The concept of table algebra in the title is a real nonsingular generalized table algebra in the sense of [Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114 (1999) 29-60]. In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too. This leads to the natural question which properties of association schemes stay valid for table algebras. For instance,
more » ... e prove the Second Isomorphism Theorem and the Jordan-Holder's theorem for standard table algebras.
doi:10.1016/j.disc.2007.08.014 fatcat:dhuop3ozmncezcczjpcdgbbvim