The geometry monoid of left self-distributivity

Abstract

We develop a counterpart to Garside's analysis of the braid monoid B n + relevant for the monoid M LD that describes the geometry of the left self-distributivity identity. The monoid M LD extends B ∞ +, of which it shares many properties, with the exception that it is not a direct limit of finitely generated monoids. By introducing a convenient local version of the fundamental elements Δ, we prove that right least common multiples exist in M LD , and, more generally, that M LD resembles a generalized Artin monoid.