Quotient structures, homomorphisms, and partial wreath products in reality-based algebras

Abstract

Homomorphisms and quotient structures of reality-based algebras are presented and described; related central idempotents and quotient sets are characterized; and the extent to which a homomorphism preserves the given anti-automorphisms of the algebras is determined. The notion of a partial wreath product, an algebraic abstraction of the wedge product of association schemes, is developed. Prototypical results previously obtained for various special cases (including table algebras and commutative C-algebras) are thus uniformly generalized.