An Algebraic Duality Theory for Multiplicative Unitaries
Doplicher, S. ; Pinzari, C. ; Roberts, J. E.
arXiv, 0001096 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-01-17
Classification:  Mathematics - Operator Algebras,  Mathematical Physics,  Mathematics - Functional Analysis,  Mathematics - Quantum Algebra 
@article{0001096,
     author = {Doplicher, S. and Pinzari, C. and Roberts, J. E.},
     title = {An Algebraic Duality Theory for Multiplicative Unitaries},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0001096}
}

Doplicher, S.; Pinzari, C.; Roberts, J. E. An Algebraic Duality Theory for Multiplicative Unitaries. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0001096/