A generalization of Coxeter groups, root systems, and Matsumoto's theorem
Quantum Algebra
2007-05-23 v1 Group Theory
Abstract
The root systems appearing in the theory of Lie superalgebras and Nichols algebras admit a large symmetry extending properly the one coming from the Weyl group. Based on this observation we set up a general framework in which the symmetry object is a groupoid. We prove that in our context the groupoid is generated by reflections and Coxeter relations. This answers a question of Serganova. Our weak version of the exchange condition allows us to prove Matsumoto's theorem. Therefore the word problem is solved for the groupoid.
Cite
@article{arxiv.math/0610823,
title = {A generalization of Coxeter groups, root systems, and Matsumoto's theorem},
author = {I. Heckenberger and H. Yamane},
journal= {arXiv preprint arXiv:math/0610823},
year = {2007}
}
Comments
16 pages