Set theoretic Yang Baxter operators
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Set-theoretic Yang-Baxter operators and their deformations Michael Eisermann Institut Fourier, Universit e Grenoble www-fourier.ujf-grenoble.fr/˜eiserm January 5, 2009 AMS–MAA Joint Mathematics Meetings in Washington DC Special Session on Algebraic Structures in Knot Theory 1/24 Overview 1 Braid groups and Yang-Baxter representations Artin's braid group Yang-Baxter representations Set-theoretic operators 2 Yang-Baxter deformations Yang-Baxter deformations Yang-Baxter cohomology Infinitesimal deformations 3 Yang-Baxter cohomology of racks Yang-Baxter cohomology of racks The diagonal cochain complex The quasi-diagonal cochain complex 4 Conclusion and open questions 2/24 Artin's braid group (1925) Braids form a group: * = = Standard generators: s i = ... ... i i+1 Obvious relations: = , = Theorem (Artin 1925) The group B n of braids on n strands is presented by B n = ? s 1 , . . . , s n?1 ? ? ? ? s i s j s i = s j s i s j if |i? j| = 1 s i s j = s i s j if |i? j| ≥ 2 ? .
Voir
- parameter infinitesimal
- deformations
- diagonal cochains
- theoretic yang
- complete deformations
- over z
- over
- artin's braid
- every yang
- open question
