Duality maps of finite abelian groups and their applications to spin models
This paper is concerned with the following concept for finite abelian groups: A duality map on the Bose-Mesner algebra spanned by the adjacency matrices of the group elements is equivalent to an isomorphism between the group and its characters, according to which the character table becomes symmetric. The authors call such isomorphism a duality map of the group, and give a classification of duality maps of finite abelian groups. Moreover, they show that if a spin model of some finite abelian group \(X\) generates the Bose-Mesner algebra of \(X\), then \(X\) is either cyclic or \(X\) is the Klein four group.
scientific article; zbMATH DE number 1228559