Details
| Original language | English |
|---|---|
| Pages (from-to) | 1112-1128 |
| Number of pages | 17 |
| Journal | Journal of Pure and Applied Algebra |
| Volume | 213 |
| Issue number | 6 |
| Publication status | Published - 1 Jun 2009 |
| Externally published | Yes |
Abstract
We adapt the generalization of root systems by the second author and H. Yamane to the terminology of category theory. We introduce Cartan schemes, associated root systems and Weyl groupoids. After some preliminary general results, we completely classify all finite Weyl groupoids with at most three objects. The classification yields the result that there exist infinitely many "standard", but only 9 "exceptional" cases.
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Pure and Applied Algebra, Vol. 213, No. 6, 01.06.2009, p. 1112-1128.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Weyl groupoids with at most three objects
AU - Cuntz, M.
AU - Heckenberger, I.
N1 - Funding information: We want to thank G. Malle for providing us with Example 3.2 , and H.-J. Schneider for many interesting discussions on the subject and for his help in searching for a good terminology. I.H. is supported by the German Research Foundation (DFG) via a Heisenberg fellowship.
PY - 2009/6/1
Y1 - 2009/6/1
N2 - We adapt the generalization of root systems by the second author and H. Yamane to the terminology of category theory. We introduce Cartan schemes, associated root systems and Weyl groupoids. After some preliminary general results, we completely classify all finite Weyl groupoids with at most three objects. The classification yields the result that there exist infinitely many "standard", but only 9 "exceptional" cases.
AB - We adapt the generalization of root systems by the second author and H. Yamane to the terminology of category theory. We introduce Cartan schemes, associated root systems and Weyl groupoids. After some preliminary general results, we completely classify all finite Weyl groupoids with at most three objects. The classification yields the result that there exist infinitely many "standard", but only 9 "exceptional" cases.
UR - http://www.scopus.com/inward/record.url?scp=60449108664&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2008.11.009
DO - 10.1016/j.jpaa.2008.11.009
M3 - Article
AN - SCOPUS:60449108664
VL - 213
SP - 1112
EP - 1128
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 6
ER -