Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 4536-4558 |
| Seitenumfang | 23 |
| Fachzeitschrift | Journal of algebra |
| Jahrgang | 319 |
| Ausgabenummer | 11 |
| Publikationsstatus | Veröffentlicht - 1 Juni 2008 |
| Extern publiziert | Ja |
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].
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Journal of algebra, Jahrgang 319, Nr. 11, 01.06.2008, S. 4536-4558.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -