Lie Groups, Lie Algebras and some applications in Physics

Abstract

Given a Lie algebra g and its complexi_cation gC; the representations of gC are isomorphic to those of g. Moreover, if g is the corresponding Lie algebra of a connected and simply connected Lie group G then the representations of the Lie group in question are isomorphic to those of gC. This thesis explains the basic concepts of Lie groups and Lie algebras. Further, the basic representation theory of Lie groups and Lie algebras, particularly those of semisimple Lie algebras is discussed. In addition, an exposition of a method of constructing induced representations, with the particular case of the Poincaré group and an application in Physics is given. Finally, some physical applications of Lie groups and Lie algebras are outlined and discussed.