A Coassociative C∗-Quantum Group with Non-Integral Dimensions
نویسنده
چکیده
By weakening the counit and antipode axioms of a C∗-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C∗Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every weak C∗-Hopf algebra has a dual which is again a weak C∗-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We shortly discuss applications to amalgamated crossed products, doubles, and quantum chains. E-mail: [email protected] Supported by the Hungarian Scientific Research Fund, OTKA T 016 233 E-mail: [email protected] Supported by the Hungarian Scientific Research Fund, OTKA–1815.
منابع مشابه
Weak C∗-hopf Algebras: the Coassociative Symmetry of Non-integral Dimensions
By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C∗-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C∗-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplica...
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