Complex Clifford Algebras

Abstract

In this chapter we describe in detail the structure of complex Clifford algebras, i.e. of Clifford algebras associated with finite dimensional complex vector spaces with a scalar product. Considerable attention is given to the relations between representations of Clifford algebras associated with vector spaces of adjacent dimension. We exhibit three types of extensions of representations and the recurrence properties of the associated inner products. The groups of automorphisms of the inner products are also derived.