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

Józef H. Przytycki , Xiao Wang

Abstract

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 paper). 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 paper). We show that they are equivalent. The "graphic" homology is also defined for pre-Yang-Baxter operators, and we give some examples of its 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.
Author Józef H. Przytycki (FMPI / IM)
Józef H. Przytycki,,
- Institute of Mathematics
, Xiao Wang
Xiao Wang,,
-
Journal seriesJournal of Knot Theory and Its Ramifications, ISSN 0218-2165, (A 20 pkt)
Issue year2018
Vol27
No7
Pages1-15
Publication size in sheets0.7
Keywords in Englishhomology, pre-cubical module, pre-simplicial module, torsion, Yang-Baxter operators
DOIDOI:10.1142/S0218216518410134
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, 13-11-2018, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, 13-11-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.363 (2) - 2016=0.453 (5)
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