Solutions of the Yang–Baxter equation associated with a left brace

David Bachiller; Ferran Cedó; Eric Jespers

doi:10.1016/j.jalgebra.2016.05.024

Solutions of the Yang–Baxter equation associated with a left brace

David Bachiller, Ferran Cedó, Eric Jespers

Research output: Contribution to journal › Article › Research › peer-review

42 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. Given a left brace B, a method is given to construct explicitly all the non-degenerate involutive set-theoretic solutions (X,r) of the Yang–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B. This method depends entirely on the brace structure of B.

Original language	English
Pages (from-to)	80-102
Journal	Journal of Algebra
Volume	463
DOIs	https://doi.org/10.1016/j.jalgebra.2016.05.024
Publication status	Published - 1 Oct 2016

Keywords

Brace
Set-theoretic solution
Yang–Baxter equation

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10.1016/j.jalgebra.2016.05.024

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title = "Solutions of the Yang–Baxter equation associated with a left brace",

abstract = "{\textcopyright} 2016 Elsevier Inc. Given a left brace B, a method is given to construct explicitly all the non-degenerate involutive set-theoretic solutions (X,r) of the Yang–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B. This method depends entirely on the brace structure of B.",

keywords = "Brace, Set-theoretic solution, Yang–Baxter equation",

author = "David Bachiller and Ferran Ced{\'o} and Eric Jespers",

year = "2016",

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doi = "10.1016/j.jalgebra.2016.05.024",

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AU - Bachiller, David

AU - Cedó, Ferran

AU - Jespers, Eric

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N2 - © 2016 Elsevier Inc. Given a left brace B, a method is given to construct explicitly all the non-degenerate involutive set-theoretic solutions (X,r) of the Yang–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B. This method depends entirely on the brace structure of B.

AB - © 2016 Elsevier Inc. Given a left brace B, a method is given to construct explicitly all the non-degenerate involutive set-theoretic solutions (X,r) of the Yang–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B. This method depends entirely on the brace structure of B.

KW - Brace

KW - Set-theoretic solution

KW - Yang–Baxter equation

U2 - 10.1016/j.jalgebra.2016.05.024

DO - 10.1016/j.jalgebra.2016.05.024

M3 - Article

SN - 0021-8693

VL - 463

SP - 80

EP - 102

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Solutions of the Yang–Baxter equation associated with a left brace

Abstract

Keywords

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