Fusion algebras with negative structure constants

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Original languageEnglish
Pages (from-to)4536-4558
Number of pages23
JournalJournal of algebra
Volume319
Issue number11
Publication statusPublished - 1 Jun 2008
Externally publishedYes

Abstract

We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with C and that their characters satisfy orthogonality relations. Then we define the proper notion of subrings and factor rings for such algebras. For certain algebras R we prove the existence of a ring R with nonnegative structure constants such that R is a factor ring of R. We give some examples of interesting factor rings of the representation ring of the quantum double of a finite group. Then, we investigate the algebras associated to Hadamard matrices. For an n × n-matrix the corresponding algebra is a factor ring of a subalgebra of Z [(Z / 2 Z)n - 2].

Keywords

    Fusion algebra, Hadamard matrix, Table algebra

ASJC Scopus subject areas

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Fusion algebras with negative structure constants. / Cuntz, Michael.
In: Journal of algebra, Vol. 319, No. 11, 01.06.2008, p. 4536-4558.

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Cuntz M. Fusion algebras with negative structure constants. Journal of algebra. 2008 Jun 1;319(11):4536-4558. doi: 10.1016/j.jalgebra.2008.02.031
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