Higman-Neumann-Neumann extension and embedding theorems for Leibniz algebras

In this work we introduce the Higman-Neumann-Neumann (HNN)- extensions and the appropriate embedding theorems for dialgebras and Leibniz algebras. Due to the importance of the connection between the dialgebras and Leibniz algebras and the relationship between associative algebras and Lie algebras, w...

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Detalles Bibliográficos
Autor: Zargeh, Chia
Tipo de recurso: tesis doctoral
Fecha de publicación:2018
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/17252
Acceso en línea:http://hdl.handle.net/10347/17252
Access Level:acceso abierto
Palabra clave:Materias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie
Materias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativas
Descripción
Sumario:In this work we introduce the Higman-Neumann-Neumann (HNN)- extensions and the appropriate embedding theorems for dialgebras and Leibniz algebras. Due to the importance of the connection between the dialgebras and Leibniz algebras and the relationship between associative algebras and Lie algebras, we recall the theory of Groebner-Shirshov bases, and the Composition-Diamond Lemma in associative algebras and Lie algebras, as well as the theory of Groebner-Shirshov bases for dialgebras. As an application of the HNN-extensions of dialgebras and Leibniz algebras, we provide embedding theorems for dialgebras and Leibniz algebras, respectively: every dialgebra embeds inside its any HNN-extension and every Leibniz algebra embeds inside its any HNN-extension.