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...

Descripción completa

Detalles Bibliográficos
Autor: Páez Guillán, María Pilar
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
id ES_19c16f84b2b4c00a72a895f067bbb622
oai_identifier_str oai:minerva.usc.gal:10347/27419
network_acronym_str ES
network_name_str España
repository_id_str
spelling Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapasPáez Guillán, María PilarMaterias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativasMaterias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de LieMaterias::Investigación::12 Matemáticas::1201 Algebra::120107 Algebra homologicaThe 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.Ladra González, ManuelKaygorodov, IvanUniversidade de Santiago de Compostela. Escola de Doutoramento Internacional (EDIUS)20212021-01-0120212021-01-01doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/10347/27419reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/274192026-06-15T12:47:27Z
dc.title.none.fl_str_mv Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
title Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
spellingShingle Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
Páez Guillán, María Pilar
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
title_short Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
title_full Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
title_fullStr Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
title_full_unstemmed Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
title_sort Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
dc.creator.none.fl_str_mv Páez Guillán, María Pilar
author Páez Guillán, María Pilar
author_facet Páez Guillán, María Pilar
author_role author
dc.contributor.none.fl_str_mv Ladra González, Manuel
Kaygorodov, Ivan
Universidade de Santiago de Compostela. Escola de Doutoramento Internacional (EDIUS)
dc.subject.none.fl_str_mv 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
topic 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
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv http://hdl.handle.net/10347/27419
url http://hdl.handle.net/10347/27419
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869404064839630848
score 15,81155

Similares en LA Referencia