RT Dissertation/Thesis
T1 Restricted Lie (super)algebras, central extensions of non-associative algebras and some tapas
A1 Páez Guillán, María Pilar
K1 Restricted Lie algebra
K1 lattice of restricted subalgebras
K1 restricted Lie superalgebra
K1 non-abelian tensor product
K1 central extension
K1 automated proving and discovery
AB The general framework of this dissertation is the theory of non-associativealgebras. We tackle diverse problems regarding restricted Lie algebras and superalgebras, central extensions ofdifferent classes of algebras and crossed modules of Lie superalgebras. Namely, we study the relations betweenthe structural properties of a restricted Lie algebra and those of its lattice of restricted subalgebras; we define anon-abelian tensor product for restricted Lie superalgebras and for graded ideal crossed submodules of a crossedmodule of Lie superalgebras, and explore their properties from structural, categorical and homological points ofview; we employ central extensions to classify nilpotent bicommutative algebras; and we compute centralextensions of the associative null-filiform algebras and of axial algebras. Also, we include a final chapter devoted tocompare the two main methods (Rabinowitsch's trick and saturation) to introduce negative conditions in thestandard procedures of the theory of automated proving and discovery.
YR 2021
FD 2021
LK http://hdl.handle.net/10347/27419
UL http://hdl.handle.net/10347/27419
LA eng
DS Minerva
RD 28 abr 2026