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From actions of an abelian group on itself to left braces

Part of: Groups and algebras in quantum theory Hopf algebras, quantum groups and related topics Radicals and radical properties of rings

Published online by Cambridge University Press:  09 January 2025

A. BALLESTER–BOLINCHES Open the ORCID record for A. BALLESTER–BOLINCHES [Opens in a new window] ,
R. ESTEBAN–ROMERO Open the ORCID record for R. ESTEBAN–ROMERO [Opens in a new window] ,
L. A. KURDACHENKO Open the ORCID record for L. A. KURDACHENKO [Opens in a new window]  and
V. PÉREZ–CALABUIG
A. BALLESTER–BOLINCHES
Affiliation:
Departament de Matemàtiques, Universitat de València Dr. Moliner, 50, 46100 Burjassot, València, Spain. e-mails: Adolfo.Ballester@uv.es, Ramon.Esteban@uv.es
R. ESTEBAN–ROMERO
Affiliation:
Departament de Matemàtiques, Universitat de València Dr. Moliner, 50, 46100 Burjassot, València, Spain. e-mails: Adolfo.Ballester@uv.es, Ramon.Esteban@uv.es
L. A. KURDACHENKO
Affiliation:
Department of Algebra and Geometry, Oles Honchar Dnipro National University Science ave., 72, Dnipro 49095, Ukraine. e-mail: lkurdachenko@gmail.com
V. PÉREZ–CALABUIG
Affiliation:
Departament de Matemàtiques, Universitat de València Dr. Moliner, 50, 46100 Burjassot, València, Spain. e-mail: Vicent.Perez-Calabuig@uv.es
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Abstract

We present a construction of left braces of right nilpotency class at most two based on suitable actions of an abelian group on itself with an invariance condition. This construction allows us to recover the construction of a free right nilpotent one-generated left brace of class two.

MSC classification

Primary: 16T25: Yang-Baxter equations
Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings 81R50: Quantum groups and related algebraic methods

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 178 , Issue 1 , January 2025 , pp. 65 - 79
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

Part of this research was carried out in the Departament de Matemàtiques, Universitat de València; Dr. Moliner, 50, 46100 Burjassot, València, Spain.

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