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Journal of the London Mathematical Society 1994 49(3):463-476; doi:10.1112/jlms/49.3.463
© 1994 by London Mathematical Society
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© The London Mathematical Society

Modular Theory and Bogoliubov Automorphisms of Clifford Algebras

P. L. Robinson

Department of Mathematics, University of Florida Gainesville, Florida 32611, USA

Received 12 March 1992.

Let {pi}c be a covariance C quasifree representation of the Clifford algebra over a real Hilbert space on which I + C2 is invertible. We determine explicitly the modular data for {pi}c and show that a Bogoliubov automorphism is weakly inner for {pi}c if and only if its generating orthogonal transformation lies in the Blattner group. We employ a model in which all quasifree representations act on one canonical Hilbert space, exhibiting the property that the modular conjugation is independent of C. This refines earlier work of Carey, Shale and Stinespring.


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