2005/09/22 by Adrian Tanasă, Adrian Tanasa, Tanasa, Adrian
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.hep-th/0509174
168 pages, 3 figures, PhD thesis
arxiv created 2005/09/22 · openalex publication_date 2005/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of deformations and contractions of these algebraic structures. We then concentrate on a particular such Lie algebra of order 3 which extends in a non-trivial way the Poincaré algebra, this extension being different of the supersymmetric extension. We then focus on the construction of a field theoretical model based on this algebra, the \it cubic supersymmetry (\it 3SUSY). For this purpose we obtain bosonic multiplets with whom we construct invariant Lagrangians. We then study the compatibility between this new symmetry and the abelian gauge symmetry. Furthermore, the analyse of possible interactions shows that interactions terms are not allowed by the cubic supersymmetry invariance. Finally we establish results regarding the extension in arbitrary dimensions of our model.