A covering theory for non-involutive set-theoretic solutions to the Yang-Baxter equation
type: Item
instance of: scholarly article
title: A covering theory for non-involutive set-theoretic solutions to the Yang-Baxter equation
zbMATH Open document ID: 1450.16024
author: Wolfgang Rump
published in: Journal of Algebra
publication date: 2018-12-14T00:00:00Z
Mathematics Subject Classification ID: 16T25
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 6993581
zbMATH Keywords: Yang-Baxter map
zbMATH Keywords: brace
zbMATH Keywords: cycle set
zbMATH Keywords: matched pair
zbMATH Keywords: skew-brace
zbMATH Keywords: structure group
zbMATH Keywords: quandle
zbMATH Keywords: cycle group
zbMATH Keywords: covering
zbMATH Keywords: Garside group
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2018.11.007
OpenAlex ID: W2900770265
cites work: From racks to pointed Hopf algebras
cites work: Hopf braces and Yang-Baxter operators
cites work: Counterexample to a conjecture about braces.
cites work: On groups of \(I\)-type and involutive Yang-Baxter groups
cites work: Komplementäre Halbgruppen. Eine Darstellungstheorie
cites work: Uniqueness of hopf galois structure for separable field extensions
cites work: Q3436063
cites work: Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles
cites work: REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS
cites work: Retractability of set theoretic solutions of the Yang-Baxter equation
cites work: Involutive Yang-Baxter groups
cites work: Fixed-point free endomorphisms and Hopf Galois structures
cites work: Garside Groups and Yang–Baxter Equation
cites work: Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
cites work: Groupes de Garside
cites work: Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs.
cites work: Garside families and Garside germs
cites work: On some unsolved problems in quantum group theory
cites work: The Centers of a Radical Ring
cites work: Pseudoeffect algebras. I: Basic properties
cites work: Homological characterization of the unknot
cites work: Quandle coverings and their Galois correspondence
cites work: On rack cohomology.
cites work: Set-theoretical solutions to the quantum Yang-Baxter equation
cites work: A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation.
cites work: Erratum: Biquandles of small size and some invariants of virtual and welded knots
cites work: RACKS AND LINKS IN CODIMENSION TWO
cites work: Biquandles and virtual links
cites work: Abelian Hopf Galois structures on prime-power Galois field extensions
cites work: Braided compact closed categories with applications to low dimensional topology
cites work: Noetherian Properties of Skew Polynomial Rings with Binomial Relations
cites work: Skew polynomial rings with binomial relations
cites work: Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity
cites work: Multipermutation solutions of the Yang-Baxter equation
cites work: Semigroups of \(I\)-type
cites work: Hopf Galois theory for separable field extensions
cites work: Skew braces and the Yang–Baxter equation
cites work: Monoids and groups of I-type.
cites work: A classifying invariant of knots, the knot quandle
cites work: Q4317887
cites work: Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
cites work: On the set-theoretical Yang-Baxter equation
cites work: A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
cites work: Braces, radical rings, and the quatum Yang-Baxter equation.
cites work: \(L\)-algebras, self-similarity, and \(l\)-groups
cites work: Non-commutative logical algebras and algebraic quantales
cites work: Q5253614
cites work: Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation
cites work: Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation.
cites work: Homological properties of Sklyanin algebras
cites work: Yang-Baxter maps and integrable dynamics
cites work: Classical solutions of the quantum Yang-Baxter equation
cites work: Quantales and (noncommutative) linear logic
Wikidata QID: Q128887602

A covering theory for non-involutive set-theoretic solutions to the Yang-Baxter equation (DOI)
DOI: 10.1016/J.JALGEBRA.2018.11.007