Higman-Neumann-Neumann extension and embedding theorems for Leibniz algebras
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http://hdl.handle.net/10347/17252
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Título: | Higman-Neumann-Neumann extension and embedding theorems for Leibniz algebras |
Autor/a: | Zargeh, Chia |
Dirección/Titoría: | Shahryari, Mohammad Ladra González, Manuel |
Centro/Departamento: | Universidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS) Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía Universidade de Santiago de Compostela. Programa de Doutoramento en Matemáticas |
Palabras chave: | Álgebras de Leibniz y de Lie | Diálgebras | Bases de Groebner-Shirshov | Extensiones HNN | Teoremas de encaje | |
Data: | 2018 |
Resumo: | 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. |
URI: | http://hdl.handle.net/10347/17252 |
Dereitos: | Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
Coleccións
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- Área de Ciencias [957]
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