RT Dissertation/Thesis
T1 Categorical-algebraic methods in non-commutative and non-associative algebra
A1 García-Martínez, Xabier
K1 Categorical algebra
K1 Non-associative algebras
K1 semi-abelian categories
K1 (co)homology theory
AB The objective of this dissertation is twofold: firstly to use categorical and algebraic methods to study homological properties of some of the aforementioned semi-abelian, non-associative structures and secondly to use categorical and algebraic methods to study categorical properties and provide categorical characterisations of some well-known algebraic structures. On one hand, the theory of universal central extensions together with the non-abelian tensor product will be studied and used to explicitly calculate some homology groups and some problems about universal enveloping algebras and actions will be solved. On the other hand, we will focus on giving categorical characterisations of some algebraic structures, such as a characterisation of groups amongst monoids, of cocommutative Hopf algebras amongst cocommutative bialgebras and of Lie algebras amongst alternating algebras.
YR 2017
FD 2017
LK http://hdl.handle.net/10347/16431
UL http://hdl.handle.net/10347/16431
LA eng
DS Minerva
RD 24 abr 2026