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
Autores: Lebed, Victoria, Vendramin, Claudio Leandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/89065
Acceso en línea:http://hdl.handle.net/11336/89065
Access Level:acceso abierto
Palabra clave:BRACE
COHOMOLOGY
CYCLE SET
EXTENSION
YANG-BAXTER EQUATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.