Ladra González, ManuelKaygorodov, IvanPáez Guillán, María Pilar2022-01-262022-01-262021http://hdl.handle.net/10347/27419The 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Restricted Lie algebralattice of restricted subalgebrasrestricted Lie superalgebranon-abelian tensor productcentral extensionautomated proving and discoveryMaterias::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 homologicadoctoral thesisopen access