HYPERIDENTITIES IN SYMMETRIC GRAPH ALGEBRAS

Abstract

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of typ (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A graph G =(V,E) is called a symmetric graph if the graph algebra A(G) satisfies the equation xy ≈ x(yx). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A. In this paper we characterize symmetric graph algebras, identities and hyperidentities in symmetric graph algebras.