Details
| Original language | English |
|---|---|
| Pages (from-to) | 4536-4558 |
| Number of pages | 23 |
| Journal | Journal of algebra |
| Volume | 319 |
| Issue number | 11 |
| Publication status | Published - 1 Jun 2008 |
| Externally published | Yes |
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
- Mathematics(all)
- Algebra and Number Theory
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of algebra, Vol. 319, No. 11, 01.06.2008, p. 4536-4558.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Fusion algebras with negative structure constants
AU - Cuntz, Michael
PY - 2008/6/1
Y1 - 2008/6/1
N2 - 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].
AB - 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].
KW - Fusion algebra
KW - Hadamard matrix
KW - Table algebra
UR - http://www.scopus.com/inward/record.url?scp=42649096288&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2008.02.031
DO - 10.1016/j.jalgebra.2008.02.031
M3 - Article
AN - SCOPUS:42649096288
VL - 319
SP - 4536
EP - 4558
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
IS - 11
ER -