Invariante de Makar-Limanov de certas hipersuperfícies algébricas

• Ano de defesa: 2014
• Autor(a) principal: Diniz., Renato dos Santos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós Graduação em Matemática; UFPB
• Palavras-chave em Português: Matemática; Hipersuperfícies algébricas; Invariante de Derksen; Invariante de Makar-Limanov; Mathematics; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7384

The Makar-Limanov invariant ML(B) of an a-ne k-algebra B (with k a -eld, which will be typically assumed to be of characteristic zero) is a very important invariant, defined in terms of the kernels of suitable derivations of B called locally nilpotent derivations. The theme has connections to various central problems in Commutative Algebra, for instance, the Jacobian Conjecture, the Fourteenth Hilbert's Problem, and the Cancellation Problem, and has been investigated by many authors. In this work, after the presentation of basic concepts and results, our main goal is the explicit obtainment of the structure of ML(B) (as a k-algebra) when B is the coordinate ring of certain special a-ne algebraic hypersurfaces, to wit, the so-called Danielewski surfaces, as well as the famous Makar-Limanov 3-fold defined by x + x2y + z2 + t3 = 0.