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Equivalence of two definitions of set-theoretic Yang-Baxter homology

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arxiv 1611.01178 v1 pith:DLAS64AJ submitted 2016-11-03 math.GT

Jozef H. Przytycki , Xiao Wang This is my paper · ORCID
classification math.GT
keywords homologydefinedgraphicoperatorsyang-baxterarticlecallpre-yang-baxter
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In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang-Baxter operators(we will call it the "algebraic" version in this article). In 2012, Przytycki defined another homology theory for pre-Yang-Baxter operators which has a nice graphic visualization(we will call it the "graphic" version in this article). We show that they are equivalent. The "graphic" homology is also defined for pre-Yang-Baxter operators, and we give some examples of it's one-term and two-term homologies. In the two-term case, we have found torsion in homology of Yang-Baxter operator that yields the Jones polynomial.

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