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An Algebraic Duality Theory for Multiplicative Unitaries

S. Doplicher·C. Pinzari·J. E. Roberts
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Abstract

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality Theorem characterizes abstractly C*-algebras acted on by unital endomorphisms that are intrinsically related to the regular representation of a multiplicative unitary. The relevant C*-algebras turn out to be simple and indeed separable if the corresponding multiplicative unitaries act on a separable Hilbert space. A categorical analogue provides internal characterizations of minimal representation categories of a multiplicative unitary. Endomorphisms of the Cuntz algebra related algebraically to the grading are discussed as is the notion of braided symmetry in a tensor C*-category.

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BibTeXRIS

S. Doplicher, C. Pinzari, J. E. Roberts. 2001-01-10. An Algebraic Duality Theory for Multiplicative Unitaries. https://arxiv.org/abs/math/0001096

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