Clifford Algebraic Representations of SU(n)

The SU(n) groups are Lie groups defined as the set of all unitary n-by-n matrices with determinant 1, whose operation is multiplication. Although defined in terms of matrices, these groups are abstract mathematical structures, and are thus indepenent of their representation. One representation of SU(n), often used in the standard model of particle theory, constructs the elements using Clifford Algebra. This representation has been shown to be valid for SU(3), but higher dimensions remain unexplored. We investigate such representations of the SU(n) groups.