The geometry monoid of left self-distributivity

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• 作者：Dehornoy ; Patrick
• 关键词：20F36 ; 20N02
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2001
• 出版时间：June 25, 2001
• 年：2001
• 卷：160
• 期：2-3
• 页码：123-156
• 全文大小：267 K

文摘

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.