Skew braces: a brief survey (Q6611821)

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scientific article; zbMATH DE number 7919707

Language	Label	Description	Also known as
English	Skew braces: a brief survey	scientific article; zbMATH DE number 7919707

Statements

scholarly article

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Skew braces: a brief survey (English)

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publication date

27 September 2024

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zbMATH Keywords

skew brace

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Yang-Baxter

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MaRDI profile type

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Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces

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Enumeration of set-theoretic solutions to the Yang–Baxter equation

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Counterexample to a conjecture about braces.

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Solutions of the Yang–Baxter equation associated to skew left braces, with applications to racks

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Solutions of the Yang-Baxter equation associated with a left brace.

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Asymmetric product of left braces and simplicity; new solutions of the Yang–Baxter equation

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A characterization of finite multipermutation solutions of the Yang-Baxter equation

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Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation

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Triply factorised groups and the structure of skew left braces

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Rota-Baxter groups, skew left braces, and the Yang-Baxter equation

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A non-affine nilvariety

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Growth series of finite extensions of \(Z^ n \)are rational

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Introduction to noncommutative algebra.

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AFFINE STRUCTURES ON NILMANIFOLDS

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Solubility criteria for Hopf-Galois structures

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A Criterion for Decomposabilty in QYBE

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Skew left braces with non-trivial annihilator

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REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS

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Left Braces: Solutions of the Yang-Baxter Equation

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Braces and symmetric groups with special conditions

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Braces and the Yang-Baxter equation

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An abundance of simple left braces with abelian multiplicative Sylow subgroups

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Every finite abelian group is a subgroup of the additive group of a finite simple left brace

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Primitive set-theoretic solutions of the Yang–Baxter equation

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Involutive Yang-Baxter groups

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Skew left braces of nilpotent type

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Garside Groups and Yang–Baxter Equation

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Left orders in Garside groups

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Ordered groups and topology

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Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs.

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Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries

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Set-theoretical solutions to the quantum Yang-Baxter equation

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A counterexample to the unit conjecture for group rings

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A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation

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Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups

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Semigroups of \(I\)-type

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Set-theoretic solutions of the Yang-Baxter equation, graphs and computations

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Matched pairs approach to set theoretic solutions of the Yang-Baxter equation.

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Finite skew braces with solvable additive group

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Skew braces and the Yang–Baxter equation

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Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group

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Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group

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Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation

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Monoids and groups of I-type.

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On geometric aspects of diffuse groups. With an appendix by Nathan Dunfield.

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An associative left brace is a ring

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Plactic monoids: a braided approach

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On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation

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On the set-theoretical Yang-Baxter equation

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Powerful \(p\)-groups. I: Finite groups.

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On finite involutive Yang–Baxter groups

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On fundamental groups of complete affinely flat manifolds

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A Simple Example of a Torsion-Free, Non Unique Product Group

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Decomposition Theorems for Involutive Solutions to the Yang–Baxter Equation

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A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation

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Braces, radical rings, and the quatum Yang-Baxter equation.

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Classification of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation

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One-generator braces and indecomposable set-theoretic solutions to the Yang–Baxter equation

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On the passage from finite braces to pre-Lie rings

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Set-theoretic solutions of the Yang-Baxter equation and new classes of \(\mathrm{R}\)-matrices

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On skew braces (with an appendix by N. Byott and L. Vendramin)

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Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation.

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On two-sided skew braces

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Group invariants of links

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Classical solutions of the quantum Yang-Baxter equation

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Identifiers

10.1007/978-3-031-62407-0_12

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6611821

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