Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1369-1393 |
| Seitenumfang | 25 |
| Fachzeitschrift | Transactions of the American Mathematical Society |
| Jahrgang | 364 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 1 Jan. 2012 |
| Extern publiziert | Ja |
Abstract
We continue our study of Cartan schemes and their Weyl groupoids and obtain a complete list of all connected simply connected Cartan schemes of rank three for which the real roots form a finite irreducible root system. We achieve this result by providing an algorithm which determines all the root systems and eventually terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between 6 and 37. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
- Mathematik (insg.)
- Angewandte Mathematik
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in: Transactions of the American Mathematical Society, Jahrgang 364, Nr. 3, 01.01.2012, S. 1369-1393.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Finite weyl groupoids of rank three
AU - Cuntz, M.
AU - Heckenberger, I.
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We continue our study of Cartan schemes and their Weyl groupoids and obtain a complete list of all connected simply connected Cartan schemes of rank three for which the real roots form a finite irreducible root system. We achieve this result by providing an algorithm which determines all the root systems and eventually terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between 6 and 37. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.
AB - We continue our study of Cartan schemes and their Weyl groupoids and obtain a complete list of all connected simply connected Cartan schemes of rank three for which the real roots form a finite irreducible root system. We achieve this result by providing an algorithm which determines all the root systems and eventually terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between 6 and 37. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.
UR - http://www.scopus.com/inward/record.url?scp=82755183510&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2011-05368-7
DO - 10.1090/S0002-9947-2011-05368-7
M3 - Article
AN - SCOPUS:82755183510
VL - 364
SP - 1369
EP - 1393
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 3
ER -