Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
The general framework of this dissertation is the theory of non-associative algebras. We tackle diverse problems regarding restricted Lie algebras and superalgebras, central extensions of different classes of algebras and crossed modules of Lie superalgebras. Namely, we study the relations between t...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2021 |
| 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:10347/27419 |
| Acceso en línea: | http://hdl.handle.net/10347/27419 |
| Access Level: | acceso abierto |
| Palabra clave: | Materias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativas Materias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de Lie Materias::Investigación::12 Matemáticas::1201 Algebra::120107 Algebra homologica |
| Sumario: | The general framework of this dissertation is the theory of non-associative algebras. We tackle diverse problems regarding restricted Lie algebras and superalgebras, central extensions of different classes of algebras and crossed modules of Lie superalgebras. Namely, we study the relations between the structural properties of a restricted Lie algebra and those of its lattice of restricted subalgebras; we define a non-abelian tensor product for restricted Lie superalgebras and for graded ideal crossed submodules of a crossed module of Lie superalgebras, and explore their properties from structural, categorical and homological points of view; we employ central extensions to classify nilpotent bicommutative algebras; and we compute central extensions of the associative null-filiform algebras and of axial algebras. Also, we include a final chapter devoted to compare the two main methods (Rabinowitsch's trick and saturation) to introduce negative conditions in the standard procedures of the theory of automated proving and discovery. |
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