Spin groups in low dimension

The aim of his thesis is to construct matrix representations of the Lie groups Spin(n) = Spin(0, n, R) in dimensions from one to six. After we construct the double-cover of the group SO(3) using the group SU(2) in the first chapter, we will define the Clifford algebra, which we will use to construct the spin group in general. We will also describe how the spin group Spin(n) provides a double-cover of the group SO(n). Using this theory, we will then construct matrix representations of the Clifford algebra and the spin group Spin(n) in all the low dimensions listed above respectively. Apart from Clifford algebra, all arguments in this thesis will be based only on linear algebra and elementary group theory.