Details
| Original language | English |
|---|---|
| Pages (from-to) | 691-709 |
| Number of pages | 19 |
| Journal | Advances in mathematics |
| Volume | 229 |
| Issue number | 1 |
| Publication status | Published - 15 Jan 2012 |
| Externally published | Yes |
Abstract
Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E8. With little extra work we prove that also all Coxeter arrangements are inductively free.
Keywords
- Arrangement of hyperplanes, Coxeter, Inductively free, Reflection
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Advances in mathematics, Vol. 229, No. 1, 15.01.2012, p. 691-709.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Coxeter and crystallographic arrangements are inductively free
AU - Barakat, Mohamed
AU - Cuntz, Michael
PY - 2012/1/15
Y1 - 2012/1/15
N2 - Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E8. With little extra work we prove that also all Coxeter arrangements are inductively free.
AB - Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type E8. With little extra work we prove that also all Coxeter arrangements are inductively free.
KW - Arrangement of hyperplanes
KW - Coxeter
KW - Inductively free
KW - Reflection
UR - http://www.scopus.com/inward/record.url?scp=80655136994&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2011.09.011
DO - 10.1016/j.aim.2011.09.011
M3 - Article
AN - SCOPUS:80655136994
VL - 229
SP - 691
EP - 709
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
IS - 1
ER -