Clifford algebras over Hilbert C*-modules

Clifford algebras of real Hilbert C*-modules with orthonormal bases are introduced. It is showed that the C*-Clifford algebra of a real Hilbert module over a real C*-algebra is *-isomorphic to the spacial tensor product of the complexification C*-algebra and a UHF C*-algebra. The von Neumann Clifford algebra of a real Hilbert module over a von Neumann algebra is *-isomorphic to the von Neumann algebra tensor product of the complexification von Neumann algebra and the hyper-finite type II1 factor.