Details
| Original language | English |
|---|---|
| Pages (from-to) | 1369-1393 |
| Number of pages | 25 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 364 |
| Issue number | 3 |
| Publication status | Published - 1 Jan 2012 |
| Externally published | Yes |
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 subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 364, No. 3, 01.01.2012, p. 1369-1393.
Research output: Contribution to journal › Article › Research › 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 -