RT Dissertation/Thesis
T1 Leibniz cohomology in low degrees. Some structure theory of Leibniz n-algebras
A1 Turdibaev, Rustam
A2 Universidade de Santiago de Compostela. Facultade de Matemáticas. Departamento de Álxebra, 
K1 álgebras de Leibniz
K1 cohomología de Leibniz
K1 derivaciones
K1 n-álgebras de Leibniz
K1 subálgebras de Cartan y Frattini
AB In this thesis some tools to study cohomology groups of Leibniz algebras with values in itself are presented. Using Levi decomposition for semisimple Leibniz algebras we establish more precise decomposition of their cohomology groups. Close look to cohomologies in low degrees yields results on outer derivations of semisimple Leibniz algebra. Furthermore, an analogue of Jordan-Chevalley decomposition for Leibniz algebras is established. Moving to a more general object, Leibniz n-algebra a several notions of solvability and nilpotence are introduced and their invariance under derivations is established. The Frattini and Cartan subalgebras of Leibniz	n-algebras are studied. Some classical results on these subalgebras are extended to Leibniz n-algebras, while some do not. In particular, examples showing that a statement on conjugacy of Cartan subalgebras of Lie algebras, which also holds in Leibniz and n-Lie algebras, does not hold for Leibniz n-algebras are constructed.
YR 2016
FD 2016-03-08
LK http://hdl.handle.net/10347/13937
UL http://hdl.handle.net/10347/13937
LA eng
DS Minerva
RD 28 abr 2026