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Covariant representations of infinite tensor product algebras

Publication ,  Journal Article
Herman, RH; Reed, MC
Published in: Pacific Journal of Mathematics
January 1, 1972

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

Published In

Pacific Journal of Mathematics

DOI

ISSN

0030-8730

Publication Date

January 1, 1972

Volume

40

Issue

2

Start / End Page

311 / 326

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Herman, R. H., & Reed, M. C. (1972). Covariant representations of infinite tensor product algebras. Pacific Journal of Mathematics, 40(2), 311–326. https://doi.org/10.2140/pjm.1972.40.311
Herman, R. H., and M. C. Reed. “Covariant representations of infinite tensor product algebras.” Pacific Journal of Mathematics 40, no. 2 (January 1, 1972): 311–26. https://doi.org/10.2140/pjm.1972.40.311.
Herman RH, Reed MC. Covariant representations of infinite tensor product algebras. Pacific Journal of Mathematics. 1972 Jan 1;40(2):311–26.
Herman, R. H., and M. C. Reed. “Covariant representations of infinite tensor product algebras.” Pacific Journal of Mathematics, vol. 40, no. 2, Jan. 1972, pp. 311–26. Scopus, doi:10.2140/pjm.1972.40.311.
Herman RH, Reed MC. Covariant representations of infinite tensor product algebras. Pacific Journal of Mathematics. 1972 Jan 1;40(2):311–326.
Journal cover image

Published In

Pacific Journal of Mathematics

DOI

ISSN

0030-8730

Publication Date

January 1, 1972

Volume

40

Issue

2

Start / End Page

311 / 326

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics