On pseudocyclic table algebras and applications to pseudocyclic association schemes

Abstract

Pseudocyclic table algebras are generalizations of Bose-Mesner algebras of pseudocyclic association schemes. Constructions of pseudocyclic association schemes have been studied among others by Hollmann [Hh], Hollmann and Xiang [HX] and Mathon [M]. In this paper we prove some general properties of pseudocyclic association schemes via the study of pseudocyclic table algebras. In particular, we will show that subschemes and quotient schemes of pseudocyclic association schemes are also pseudocyclic association schemes, and combinatorial morphisms between any two t-pseudocyclic association schemes induce algebra homomorphisms between their Bose-Mesner algebras. Furthermore, we will prove that an algebra isomorphism between two t-pseudocyclic table algebras under some weak condition is an exact isomorphism. Properties of pseudocyclic P-polynomial table algebras will also be studied.