Matsumoto theorem for skeleta

Abstract

We present a proof of a generalization of the theorem of H.~Matsumoto on Coxeter groups. Our generalized version is applicable to "graphs admitting geometric realization". The original version of the theorem for Coxeter groups is a special case when applied to the Cayley graph and the geometric representation of a Coxeter group. Our version of Matsumoto theorem is also applicable to skeleta, graphs that were defined in the recent paper by the authors on root Lie superalgebras.

10 pages, minor change in ntroduction