Quantisização da Álgebra U(g) para uma Álgebra de Lie simples g.

Abstract

The quantum groups associated with a Lie Algebra, denoted by U_h(g) are deformations of the universal enveloping Algebra associated with the Lie algebra g, which is a Hopf Algebra. Furthermore, quantum Lie algebras L_h(g) are generalizations of Lie algebras g whose structure constants are power series in h. The L_h(g) Algebras are derivatives of the Quantized Enclosing Algebras U_h(g), with a quantum bracket that satisfies a generalization of antisymmetry. Starting from the previous concepts, in this work the quantum group U_h(g) and the quantum Lie Algebra L_h(g) will be constructed for the explicit case of the Lie Algebra Special linear Lie g=sl_2(C) and later generalized to a simple Lie Algebra over C of finite dimension.