Sobre Anéis de Lie Admitindo Automorfismos de Ordens Finitas e Álgebras de Lie Quase Nilpotentes.

• Autor(a) principal: MELO, Emerson Ferreira de
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1938
• topic: Anéis de Lie; Álgebras de Lie; Automorfismos; Quase Nilpotência; 1. Anéis de Lie 2. Álgebras de Lie 3. Automorfismos 4. Quase Nilpotente; Lie Rings; Lie Algebras; Automorphisms; Almost Nilpotency; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

In this work we present a study on Lie rings and algebras admitting an automorphism of finite order. We emphasize questions on nilpotency. We prove important results of this theory, for example the Higman, Kreknin and Kostrikin s Theorem. Furthermore, let L be a finite dimensional Lie algebra over an algebraically closed field of characteristic 0. Suppose that L admits a nilpotent Lie algebra D with n weights in L, and let m be the dimension of the Fitting null component with respect to D. Then L is almost nilpotent, namely, L contains a nilpotent subalgebra N of {m,n}-bounded codimension and of nbounded nilpotency class. If m = 0, then L is nilpotent of bounded class by a function of n. This theorem was published by E. I. Khukhro and P. Shumyatsky in the paper entitled Lie Algebras with Almost Constant-Free Derivations .