Coxeter and crystallographic arrangements are inductively free

@article{Barakat2010CoxeterAC,
  title={Coxeter and crystallographic arrangements are inductively free},
  author={Mohamed Barakat and Michael Cuntz},
  journal={Advances in Mathematics},
  year={2010},
  volume={229},
  pages={691-709}
}
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31 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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Results Citations
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31 Citations

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References

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Crystallographic arrangements: Weyl groupoids and simplicial arrangements

We introduce the simple notion of a ‘crystallographic arrangement’ and prove a one‐to‐one correspondence between these arrangements and the connected simply connected Cartan schemes for which the…

Coxeter arrangements are hereditarily free

. A Coxeter arrangement is the set of reflecting hyperplanes in the reflection representation of a finite Coxeter group. Arnold and Saito showed that every Coxeter arrangement is free. We prove that…

Finite Weyl groupoids

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…

Free arrangements of hyperplanes and supersolvable lattices

AN AXIOMATIC SETUP FOR ALGORITHMIC HOMOLOGICAL ALGEBRA AND AN ALTERNATIVE APPROACH TO LOCALIZATION

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian…

Commutative Algebra I

1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed

SINGULAR: a computer algebra system for polynomial computations

SINGULAR is a specialized computer algebra system for polynomial computations with emphasize on the needs of commutative algebra, algebraic geometry, and singularity theory, which features one of the fastest and most general implementations of various algorithms for computing standard resp.

Eléments de mathématique : groupes et algèbres de Lie

D-67653 Kaiserslautern, Germany E-mail address: cuntz@mathematik.uni-kl

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Set t = I r , the identity matrix of rank r