TY - JOUR

T1 - Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions

AU - Przytycki, Józef H.

AU - Vojtěchovský, Petr

AU - Yang, Seung Yeop

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and cycle sets. 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 compute the normalized set-theoretic Yang-Baxter homology of cyclic racks. Moreover, we explicitly calculate some two-cocycles, which can be used to classify certain families of torus links.

AB - W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and cycle sets. 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 compute the normalized set-theoretic Yang-Baxter homology of cyclic racks. Moreover, we explicitly calculate some two-cocycles, which can be used to classify certain families of torus links.

KW - cycle set

KW - normalized Yang-Baxter (co)homology theory

KW - Set-theoretical solution of Yang-Baxter equation

UR - http://www.scopus.com/inward/record.url?scp=85165195149&partnerID=8YFLogxK

U2 - 10.1142/S0218216523400217

DO - 10.1142/S0218216523400217

M3 - Article

AN - SCOPUS:85165195149

SN - 0218-2165

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

M1 - 2340021

ER -