Partial symmetry, reflection monoids and Coxeter groups

Abstract

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.

This is a completely reorganized and rewritten version of our earlier paper math/0701313v2, with a number of new results