Letters in Mathematical Physics

, Volume 38, Issue 4, pp 437–456

A coassociativeC*-quantum group with nonintegral dimensions

  • Gabriella Bòhm
  • Korníl Szlachónyi

DOI: 10.1007/BF01815526

Cite this article as:
Bòhm, G. & Szlachónyi, K. Lett Math Phys (1996) 38: 437. doi:10.1007/BF01815526


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.

Mathematics Subject Classification (1991)


Key words

Weak Hopf algebrasmultiplicative isometriesamalgamated crossed products

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Gabriella Bòhm
    • 1
  • Korníl Szlachónyi
    • 1
  1. 1.Central Research Institute for PhysicsBudapest 114Hungary