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Torus invariance for the Clifford algebra, II

Publication ,  Journal Article
Reed, MC
Published in: Journal of Functional Analysis
January 1, 1971

The structure of the representations of the infinite-dimensional Clifford algebra generated by states symmetric about a basis is studied. In particular, it is shown where they fit into the Gårding-Wightman classification. These representations have an unusual structure: the fibres are all infinite tensor product spaces, but the fibres corresponding to points on different orbits of the underlying group are different separable subspaces of the same inseparable infinite tensor product space. A procedure is given for constructing a large class of other representations of similar structure in which the torus automorphisms are unitarily implementable. In all cases the torus invariance depends on the geometric structure of the fibres, not on the underlying measure. © 1971.

Duke Scholars

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1971

Volume

8

Issue

3

Start / End Page

450 / 468

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
NLM
Reed, M. C. (1971). Torus invariance for the Clifford algebra, II. Journal of Functional Analysis, 8(3), 450–468. https://doi.org/10.1016/0022-1236(71)90006-1
Reed, M. C. “Torus invariance for the Clifford algebra, II.” Journal of Functional Analysis 8, no. 3 (January 1, 1971): 450–68. https://doi.org/10.1016/0022-1236(71)90006-1.
Reed MC. Torus invariance for the Clifford algebra, II. Journal of Functional Analysis. 1971 Jan 1;8(3):450–68.
Reed, M. C. “Torus invariance for the Clifford algebra, II.” Journal of Functional Analysis, vol. 8, no. 3, Jan. 1971, pp. 450–68. Scopus, doi:10.1016/0022-1236(71)90006-1.
Reed MC. Torus invariance for the Clifford algebra, II. Journal of Functional Analysis. 1971 Jan 1;8(3):450–468.
Journal cover image

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1971

Volume

8

Issue

3

Start / End Page

450 / 468

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics