Geodesic
On even generalized table algebras
Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 163-170.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: generalized table algebras, association schemes 
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     author = {Arad, Z. and Erez, Y. and Muzychuk, M.},
     title = {On even generalized table algebras},
     journal = {Journal of Algebraic Combinatorics},
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Arad, Z.; Erez, Y.; Muzychuk, M. On even generalized table algebras. Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 163-170. http://geodesic.mathdoc.fr/item/JAC_2003__17_2_a2/