Details
| Original language | English |
|---|---|
| Pages (from-to) | 50-69 |
| Number of pages | 20 |
| Journal | Journal of algebra |
| Volume | 574 |
| Early online date | 2 Feb 2021 |
| Publication status | Published - 15 May 2021 |
Abstract
Keywords
- Reflection group, Simplicial arrangement, Weyl group, Weyl groupoid
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 574, 15.05.2021, p. 50-69.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A bound for crystallographic arrangements
AU - Cuntz, Michael
PY - 2021/5/15
Y1 - 2021/5/15
N2 - A crystallographic arrangement is a set of linear hyperplanes satisfying a certain integrality property and decomposing the space into simplicial cones. Crystallographic arrangements were completely classified in a series of papers by Heckenberger and the author. However, this classification is based on two computer proofs checking millions of cases. In the present paper, we prove without using a computer that, up to equivalence, there are only finitely many irreducible crystallographic arrangements in each rank greater than two.
AB - A crystallographic arrangement is a set of linear hyperplanes satisfying a certain integrality property and decomposing the space into simplicial cones. Crystallographic arrangements were completely classified in a series of papers by Heckenberger and the author. However, this classification is based on two computer proofs checking millions of cases. In the present paper, we prove without using a computer that, up to equivalence, there are only finitely many irreducible crystallographic arrangements in each rank greater than two.
KW - Reflection group
KW - Simplicial arrangement
KW - Weyl group
KW - Weyl groupoid
UR - http://www.scopus.com/inward/record.url?scp=85100250719&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2021.01.028
DO - 10.1016/j.jalgebra.2021.01.028
M3 - Article
VL - 574
SP - 50
EP - 69
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -