Covariant representations of infinite tensor product algebras

In this paper myriad covariant representations of a class of C*-algebras and automorphism groups are constructed. The Hilbert spaces on which the representations are realized have an unusual structure: they are direct integrals of measurable families S(·) of Hilbert spaces over the spectrum of an abelian subalgebra of the C*-algebra; the fibre spaces S(·) are (in general) different separable subspaces of inseparable infinite tensor product spaces. The representors of the algebra and the unitary representors of the group do not decompose but act both in the fibres and on the underlying spectrum. Cases covered by this construction include the quasifree automorphisms of the Clifford algebra which leave a given basis fixed and the automorphism corresponding to charge conjugation. © 1992 Pacific Journal of Mathematics.

Duke Scholars

Author Michael C. Reed Mathematics