A generalization of Coxeter groups, root systems, and Matsumoto's theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118136The 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.16 pagesQuantum AlgebraGroup Theory20M05; 20F55; 17B20A generalization of Coxeter groups, root systems, and Matsumoto's theoremtext