Crystallographic arrangements: Weyl groupoids and simplicial arrangements

Details Crystallographic arrangements: Weyl groupoids and simplicial arrangements Crystallographic arrangements: Weyl groupoids and simplicial arrangements

2010-06-10

arxiv.org/abs/1006.1997v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

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 real roots are a finite root system (up to equivalence on both sides). We thus obtain a more accessible definition for this very large subclass of the class of simplicial arrangements for which a complete classification is known.

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