Left-Garside categories, self-distributivity, and braids

Dehornoy, Patrick

Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 189-244.

In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and Self-distributivity, Birkhaüser (2000), Chap. IX].

Classification : 18B40, 20N02, 20F36
Mots clés : Garside category, Garside monoid, self-distributivity, braid, greedy normal form, least common multiple, LD-expansion

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