The Clifford algebra and its Spin subgroup

Abstract

This thesis gives an introduction to the Clifford algebra and its Spin subgroup. We first construct the Clifford algebra before using the spinorial representation to proof its (semi)simplicity. We then construct the Spin group and determine its irreducible representations using weight theory. The reader is expected to have prior knowledge about rings and representations of groups, but all required theory will be recalled in the preliminaries.