A new approach to induction and imprimitivity results |
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Authors: | Stefaan Vaes |
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Institution: | Institute of Mathematics of Jussieu, Algèbres d’Opérateurs, Plateau 7E, 175, rue du Chevaleret, F-75014 Paris, France |
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Abstract: | Given a closed quantum subgroup of a locally compact quantum group, we study induction of unitary corepresentations of the quantum subgroup to the ambient quantum group. More generally, we study induction given a coaction of the quantum subgroup on a C*-algebra. We prove imprimitivity theorems that unify the existing theorems for actions and coactions of groups. This means that we define quantum homogeneous spaces as C*-algebras and that we prove Morita equivalence of crossed products and homogeneous spaces. We essentially use von Neumann algebraic techniques to prove these Morita equivalences between C*-algebras. |
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Keywords: | primary 22D30 secondary 46L89 46L55 46L08 |
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