Details
| Original language | English |
|---|---|
| Pages (from-to) | 77-108 |
| Number of pages | 32 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2015 |
| Issue number | 702 |
| Publication status | Published - 1 May 2015 |
| Externally published | Yes |
Abstract
Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains the list of all crystallographic arrangements, a large subclass of the class of simplicial hyperplane arrangements. Supposing that the rank is at least three, the classification yields Cartan schemes of type A and B, an infinite family of series involving the types C and D, and 74 sporadic examples.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal fur die Reine und Angewandte Mathematik, Vol. 2015, No. 702, 01.05.2015, p. 77-108.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Finite Weyl groupoids
AU - Cuntz, Michael
AU - Heckenberger, István
PY - 2015/5/1
Y1 - 2015/5/1
N2 - Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains the list of all crystallographic arrangements, a large subclass of the class of simplicial hyperplane arrangements. Supposing that the rank is at least three, the classification yields Cartan schemes of type A and B, an infinite family of series involving the types C and D, and 74 sporadic examples.
AB - Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are determined. As a consequence one obtains the list of all crystallographic arrangements, a large subclass of the class of simplicial hyperplane arrangements. Supposing that the rank is at least three, the classification yields Cartan schemes of type A and B, an infinite family of series involving the types C and D, and 74 sporadic examples.
UR - http://www.scopus.com/inward/record.url?scp=84928914685&partnerID=8YFLogxK
U2 - 10.1515/crelle-2013-0033
DO - 10.1515/crelle-2013-0033
M3 - Article
AN - SCOPUS:84928914685
VL - 2015
SP - 77
EP - 108
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 702
ER -