Fusion algebras with negative structure constants
| dc.creator | Cuntz, Michael | |
| dc.date | 2007-04-18 | |
| dc.date.accessioned | 2026-07-07T07:57:04Z | |
| dc.date.available | 2026-07-07T07:57:04Z | |
| dc.description | We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ 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 $n\times n$-matrix the corresponding algebra is a factor ring of a subalgebra of $\mathbb{Z}[{(\mathbb{Z}/2\mathbb{Z})}^{n-2}]$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0704.2384 | |
| dc.identifier | http://arxiv.org/abs/0704.2384 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127548 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 81R05; 19A49; 05B20 | |
| dc.title | Fusion algebras with negative structure constants | |
| dc.type | text |