Association schemes and fusion algebras. (An introduction)
type: Item
instance of: scholarly article
title: Association schemes and fusion algebras. (An introduction)
zbMATH Open document ID: 0790.05098
DOI: 10.1023/A:1022489416433
author: Eiichi Bannai
published in: Journal of Algebraic Combinatorics
publication date: 1994-06-22T00:00:00Z
review text: Fusion algebras are finite dimensional commutative and associative algebras (over complex number field) which appear in conformal field theory in mathematical physics. The main purpose of the reviewed paper is to start with the study of fusion algebras from a purely algebraic viewpoint. The author considers an algebraic object, which he calls fusion algebra at algebraic level, and finds its connection with another purely algebraic object, called character algebra, which is closely connected with Bose-Mesner algebras (Hecke algebras) of an association scheme. There is the matrix \(S\) in fusion algebra which plays an important role in conformal field theory. The author shows, contrary to the theory of fusion algebras in conformal field theory, that the matrix \(S\) of a fusion algebra at algebraic level is not necessarily unitary nor symmetric and gives exact characterizations of when the matrix \(S\) is unitary or symmetric in terms of the corresponding character algebra. Moreover he discusses the modular invariance of a fusion algebra since this property is very important in conformal field theory; for example the fusion algebras of well-known conformal theories have this property.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 13M99
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 482245
zbMATH Keywords: fusion algebras
zbMATH Keywords: character algebra
zbMATH Keywords: association scheme
zbMATH Keywords: modular invariance
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
cites work: Q4010723
cites work: Modular invariance of the character table of the Hamming association scheme \(H(d,q)\)
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description: scientific article; zbMATH DE number 482245