Quasi-deformations of the special linear lie algebra of degree 2 using twisted derivations.
Date
2024
Authors
Sampa, Dominique
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Journal ISSN
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Publisher
The University of Zambia
Abstract
In this dissertation we obtain quasi-deformations of the special linear Lie algebra of degree 2 over a eld F, abbreviated sl2(F). We take F to be a eld of characteristic zero. Our approach involves obtaining and deforming a linear operator representation of sl2(F) using-twisted derivations (with an endomorphism on the base algebra). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. Furthermore, we show that by choosing parameters suitably we can deform sl2(F) into the Heisenberg Lie algebra and some other 3- and 4-dimensional Lie algebras in addition to more exotic types of algebras. This is in stark contrast to the usual classical deformation schemes where sl2(F) is rigid.
Description
Thesis of Master of Science in Mathematics.