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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| 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 |
| 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. |
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