Lie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry

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dc.creatorTanasa, Adrian
dc.date2005-09-22
dc.date.accessioned2026-07-07T06:18:47Z
dc.date.available2026-07-07T06:18:47Z
dc.descriptionIn 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.
dc.description168 pages, 3 figures, PhD thesis
dc.identifierhttps://arxiv.org/abs/hep-th/0509174
dc.identifierhttp://arxiv.org/abs/hep-th/0509174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94855
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleLie subalgebras of the Weyl algebra. Lie algebras of order 3 and their application to cubic supersymmetry
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