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

Józef H. Przytycki; Petr Vojtěchovský; Seung Yeop Yang

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arXiv · 1911.03009

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

Józef H. Przytycki·Petr Vojtěchovský·Seung Yeop Yang

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Abstract

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.

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BibTeX RIS

Józef H. Przytycki, Petr Vojtěchovský, Seung Yeop Yang. 2019-11-08. Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions. https://arxiv.org/abs/1911.03009

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