Duality maps of finite abelian groups and their applications to spin models
type: Item
instance of: scholarly article
title: Duality maps of finite abelian groups and their applications to spin models
zbMATH Open document ID: 0927.05084
DOI: 10.1023/A:1008613331395
author: Etsuko Bannai
author: Akihiro Munemasa
published in: Journal of Algebraic Combinatorics
publication date: 1999-12-05T00:00:00Z
review text: 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.
reviewed by: Markus Fulmek
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 1228559
zbMATH Keywords: spin model
zbMATH Keywords: finite abelian group
zbMATH Keywords: quadratic form
zbMATH Keywords: association scheme
zbMATH Keywords: Bose-Mesner algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1228559