A family of solutions of the Yang-Baxter equation

David Bachiller; Ferran Cedó

doi:https://doi.org/10.1016/j.jalgebra.2014.05.011

A family of solutions of the Yang-Baxter equation

David Bachiller, Ferran Cedó

Department of Mathematics

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

16 Citations (Scopus)

Abstract

A new method to construct involutive non-degenerate set-theoretic solutions (X n, r(n)) of the Yang-Baxter equation, for any positive integer n, from a given solution (X, r) is presented. Furthermore, the permutation group G(Xn,r(n)) associated with the solution (X n, r(n)) is isomorphic to a subgroup of G(X,r), and in many cases G(Xn,r(n))≅G(X,r). © 2014 Elsevier Inc.

Original language	English
Pages (from-to)	218-229
Journal	Journal of Algebra
Volume	412
DOIs	https://doi.org/10.1016/j.jalgebra.2014.05.011
Publication status	Published - 15 Aug 2014

Keywords

$Yang-Baxter equation$Involutive non-degenerate solutions$Brace$IYB group
Brace
IYB group
Involutive non-degenerate solutions
Yang-Baxter equation

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title = "A family of solutions of the Yang-Baxter equation",

abstract = "A new method to construct involutive non-degenerate set-theoretic solutions (X n, r(n)) of the Yang-Baxter equation, for any positive integer n, from a given solution (X, r) is presented. Furthermore, the permutation group G(Xn,r(n)) associated with the solution (X n, r(n)) is isomorphic to a subgroup of G(X,r), and in many cases G(Xn,r(n))≅G(X,r). {\textcopyright} 2014 Elsevier Inc.",

keywords = "$Yang-Baxter equation$Involutive non-degenerate solutions$Brace$IYB group, Brace, IYB group, Involutive non-degenerate solutions, Yang-Baxter equation",

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

year = "2014",

month = aug,

day = "15",

doi = "https://doi.org/10.1016/j.jalgebra.2014.05.011",

language = "English",

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pages = "218--229",

journal = "Journal of Algebra",

issn = "0021-8693",

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T1 - A family of solutions of the Yang-Baxter equation

AU - Bachiller, David

AU - Cedó, Ferran

PY - 2014/8/15

Y1 - 2014/8/15

N2 - A new method to construct involutive non-degenerate set-theoretic solutions (X n, r(n)) of the Yang-Baxter equation, for any positive integer n, from a given solution (X, r) is presented. Furthermore, the permutation group G(Xn,r(n)) associated with the solution (X n, r(n)) is isomorphic to a subgroup of G(X,r), and in many cases G(Xn,r(n))≅G(X,r). © 2014 Elsevier Inc.

AB - A new method to construct involutive non-degenerate set-theoretic solutions (X n, r(n)) of the Yang-Baxter equation, for any positive integer n, from a given solution (X, r) is presented. Furthermore, the permutation group G(Xn,r(n)) associated with the solution (X n, r(n)) is isomorphic to a subgroup of G(X,r), and in many cases G(Xn,r(n))≅G(X,r). © 2014 Elsevier Inc.

KW - $Yang-Baxter equation$Involutive non-degenerate solutions$Brace$IYB group

KW - Brace

KW - IYB group

KW - Involutive non-degenerate solutions

KW - Yang-Baxter equation

U2 - https://doi.org/10.1016/j.jalgebra.2014.05.011

DO - https://doi.org/10.1016/j.jalgebra.2014.05.011

M3 - Article

VL - 412

SP - 218

EP - 229

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -