Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions

Autor:	Przytycki, Józef H., Vojtěchovský, Petr, Yang, Seung Yeop
Rok vydání:	2019
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology 16T25 20N05 57M27
Druh dokumentu:	Working Paper
Popis:	W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and Rump right quasigroups. J. S. Carter, M. Elhamdadi, and M. Saito, meanwhile, introduced a homology theory of set-theoretic solutions of the Yang-Baxter equation in order to define cocycle invariants of classical knots. In this paper, we introduce the normalized homology theory of an involutive right non-degenerate solution of the Yang-Baxter equation and prove that the set-theoretic Yang-Baxter homology of certain solutions can be split into the normalized and degenerated parts. Comment: 14 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.03009 Zobrazit plný text záznamu View this record from Arxiv