Cohomology and extensions of braces

Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group st...

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Detalles Bibliográficos
Autor principal: Vendramin, Leandro
Publicado: 2016
Materias:
Brace
Cohomology
Cycle set
Extension
Yang-Baxter equation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v284_n1_p191_Lebed
http://hdl.handle.net/20.500.12110/paper_00308730_v284_n1_p191_Lebed
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00308730_v284_n1_p191_Lebed
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spelling paper:paper_00308730_v284_n1_p191_Lebed2025-07-30T17:37:59Z Cohomology and extensions of braces Vendramin, Leandro Brace Cohomology Cycle set Extension Yang-Baxter equation Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups. © 2016 Mathematical Sciences Publishers. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v284_n1_p191_Lebed http://hdl.handle.net/20.500.12110/paper_00308730_v284_n1_p191_Lebed
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Brace
Cohomology
Cycle set
Extension
Yang-Baxter equation
spellingShingle Brace
Cohomology
Cycle set
Extension
Yang-Baxter equation
Vendramin, Leandro
Cohomology and extensions of braces
topic_facet Brace
Cohomology
Cycle set
Extension
Yang-Baxter equation
description Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups. © 2016 Mathematical Sciences Publishers.
author Vendramin, Leandro
author_facet Vendramin, Leandro
author_sort Vendramin, Leandro
title Cohomology and extensions of braces
title_short Cohomology and extensions of braces
title_full Cohomology and extensions of braces
title_fullStr Cohomology and extensions of braces
title_full_unstemmed Cohomology and extensions of braces
title_sort cohomology and extensions of braces
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v284_n1_p191_Lebed
http://hdl.handle.net/20.500.12110/paper_00308730_v284_n1_p191_Lebed
work_keys_str_mv AT vendraminleandro cohomologyandextensionsofbraces
_version_ 1840321607838466048

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