Equivalence of two definitions of set-theoretic Yang-Baxter homology and general Yang-Baxter homology
Józef H. Przytycki , Xiao Wang
AbstractIn 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.
|Journal series||Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, (A 20 pkt)|
|Publication size in sheets||0.7|
|Keywords in English||homology, pre-cubical module, pre-simplicial module, torsion, Yang-Baxter operators|
|Score|| = 20.0, 27-12-2018, ArticleFromJournal|
= 20.0, 27-12-2018, ArticleFromJournal
|Publication indicators||: 2017 = 0.458 (2) - 2017=0.562 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.