On one class of extensions of Lie algebras and the Casimir functions related to it

dos Santos, Moses Caires

On one class of extensions of Lie algebras and the Casimir functions related to it

Thesis / Dissertation

2009

Abstract

In chapter 1, we introduce the extensions and cohomologies of Lie algebras, followed by the lemmas of Vhitehcad and finally the Levi-decomposition theorem. In chapter 2, we introduce the "universal" extensions of the Lie algebras as originally given in [l] and classify them up to some point (where n::::; 4 as given in (l]). In Chapter 3, an alternative approach to these "universal" extensions is given, that seen in [2] and the t·wo approaches are compared and finally; In Chapter 4, the related Casimir Invariants are introduced. We attempt to further understand their algebraic properties developing the ideas of [l] and [2]. In the appendices we give some additional information that is needed to understand the text.

Keywords

Applied Mathematics

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