Fusion algebras with negative structure constants

JOURNAL OF ALGEBRA

卷:319

Article

Cuntz, Michael

关键词: fusion algebra;    table algebra;    Hadamard matrix;   

DOI  :  10.1016/j.jalgebra.2008.02.031

来源: Elsevier

【 摘 要 】

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 x n-matrix the corresponding algebra is a factor ring of a subalgebra of Z[(Z/2Z)(n-2)]. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free