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 -