A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation.

DOI10.1016/j.jpaa.2016.04.010zbMath1347.16036arXiv1508.07970OpenAlexW2963881663WikidataQ115345421 ScholiaQ115345421MaRDI QIDQ284963

Juliana García Galofre, Marco Andrés Farinati

Publication date: 18 May 2016

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.07970

zbMATH Keywords

Yang-Baxter equationHochschild homologydifferential graded bialgebrasYang-Baxter homology

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Differential graded algebras and applications (associative algebraic aspects) (16E45) Bialgebras (16T10) Yang-Baxter equations (16T25)

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Cites Work

• Unnamed Item
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• Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova.
• Retractability of set theoretic solutions of the Yang-Baxter equation
• The diamond lemma for ring theory
• Semigroups of \(I\)-type
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Homologies of algebraic structures via braidings and quantum shuffles
• Augmented biracks and their homology
• THE ALGEBRA OF RACK AND QUANDLE COHOMOLOGY
• Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
• Quandle homology groups, their Betti numbers, and virtual knots
• Twisted quandle homology theory and cocycle knot invariants