Modular Theory and Bogoliubov Automorphisms of Clifford Algebras | Zendy

Robinson P. L. | Zendy

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Modular Theory and Bogoliubov Automorphisms of Clifford Algebras

Author(s) -

Robinson P. L.

Publication year - 1994

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/49.3.463

Subject(s) - automorphism , clifford algebra , hilbert space , pure mathematics , mathematics , invertible matrix , covariance , algebra over a field , modular design , orthogonal group , group (periodic table) , transformation (genetics) , space (punctuation) , physics , computer science , chemistry , quantum mechanics , biochemistry , statistics , gene , operating system

Let π c be a covariance C quasifree representation of the Clifford algebra over a real Hilbert space on which I + C 2 is invertible. We determine explicitly the modular data for π c and show that a Bogoliubov automorphism is weakly inner for π 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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