Details
| Original language | English |
|---|---|
| Pages (from-to) | 1350-1363 |
| Number of pages | 14 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 118 |
| Issue number | 4 |
| Publication status | Published - 1 May 2011 |
| Externally published | Yes |
Abstract
We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to 'reflection groupoids' by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type An-3 completely describes the set of finite reflection groupoids of rank two with 2 n objects.
Keywords
- Arrangement of hyperplanes, Cluster algebra, Pointed Hopf algebra, Weyl groupoid
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Journal of Combinatorial Theory. Series A, Vol. 118, No. 4, 01.05.2011, p. 1350-1363.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Reflection groupoids of rank two and cluster algebras of type A
AU - Cuntz, M.
AU - Heckenberger, I.
N1 - Funding information: E-mail addresses: cuntz@mathematik.uni-kl.de (M. Cuntz), heckenberger@mathematik.uni-marburg.de (I. Heckenberger). 1 Supported by the German Research Foundation (DFG) via a Heisenberg fellowship.
PY - 2011/5/1
Y1 - 2011/5/1
N2 - We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to 'reflection groupoids' by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type An-3 completely describes the set of finite reflection groupoids of rank two with 2 n objects.
AB - We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to 'reflection groupoids' by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type An-3 completely describes the set of finite reflection groupoids of rank two with 2 n objects.
KW - Arrangement of hyperplanes
KW - Cluster algebra
KW - Pointed Hopf algebra
KW - Weyl groupoid
UR - http://www.scopus.com/inward/record.url?scp=78651408191&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2010.12.003
DO - 10.1016/j.jcta.2010.12.003
M3 - Article
AN - SCOPUS:78651408191
VL - 118
SP - 1350
EP - 1363
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
SN - 0097-3165
IS - 4
ER -