Abstract
By weakening the counit and antipode axioms of aC *-Hopf algebra and allowing for the coassociative coproduct to be nonunital, we obtain a quantum group, that we call aweak 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 finite-dimensional weakC *-Hopf algebra has a dual which is again a weakC *-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.
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Supported by the Hungarian Scientific Research Fund, OTKA T 016 233.
Supported by the Hungarian Scientific Research Fund, OTKA-1815.
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Bòhm, G., Szlachónyi, K. A coassociativeC *-quantum group with nonintegral dimensions. Lett Math Phys 38, 437–456 (1996). https://doi.org/10.1007/BF01815526
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DOI: https://doi.org/10.1007/BF01815526