Infinite dimensional Clifford algebras

Clifford algebras play an important role in many areas of mathematics andin physical applications. Clifford algebras are associative algebras which aregenerated by means of a symmetric bilinear function on a vector space. Infinitedimensional Clifford algebras are however not yet at the center of interest.Spinors and representation theory are completely known for finite dimensionalClifford algebras. The aim of this study is to investigate the representationsof infinite dimensional Clifford algebras.The idea that Clifford algebras could be represented on fractals is suggestedin the paper by Lawrynowicz and Suzuki [7], which contains some interestingideas as well as some technical errors. In this thesis, a direct representation isgiven for both finite and infinite dimensional real and complex Clifford algebrason the Cantor set. Moreover, it is proved that this representation is equivalentto Fock representation for infinite dimensional Clifford algebras.