## Characters of table algebras and applications to association schemes

- Bangteng Xu
- J. Comb. Theory, Ser. A
- 2008

1 Excerpt

- Published 2003

Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math. 114 (1999), 29–60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric.

@inproceedings{Arad2003OnEG,
title={On Even Generalized Table Algebras},
author={Zvi Arad},
year={2003}
}