Left-Garside categories, self-distributivity, and braids
Annales mathématiques Blaise Pascal, Volume 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].

DOI: 10.5802/ambp.263
Classification: 18B40, 20N02, 20F36
Keywords: Garside category, Garside monoid, self-distributivity, braid, greedy normal form, least common multiple, LD-expansion
Patrick Dehornoy 1

1 Laboratoire de Mathématiques Nicolas Oresme Université de Caen 14032 Caen France
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Patrick Dehornoy. Left-Garside categories, self-distributivity, and braids. Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 2, pp. 189-244. doi : 10.5802/ambp.263. https://ambp.centre-mersenne.org/articles/10.5802/ambp.263/

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