publication . Doctoral thesis . 2008

Simple Lie algebras, algebraic prolongations and contact structures

Bucicovschi, Orest;
Open Access
  • Published: 01 Jan 2008
  • Publisher: eScholarship, University of California
  • Country: United States
Abstract
The story starts with the result of Mukai that every complex simple finite dimensional Lie algebra has a faithful realization as a subalgebra of an algebra of polynomials with the Legendre bracket. Every such realization is determined by a unique polynomial of degree 4. This generalizes the result of Cartan that found a 14- dimensional vector space of polynomials in 5 variables which is a Lie algebra of type G₂ with respect to the Legendre bracket. To prove his result Mukai uses the notion of algebraic prolongation of a negatively graded Lie algebra. He observes that the algebraic prolongation of a graded Heisenberg Lie algebra of dimension 2d+1 is the algebra o...
Subjects
free text keywords: UCSD Mathematics. (Discipline) Dissertations, Academic
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