Quasi-deformations of the special linear lie algebra of degree 2 using twisted derivations.

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.