A Coassociative C-Quantum Group with Nonintegral Dimensions

Gabriella Bòhm, Korníl Szlachónyi

Research output: Article

90 Citations (Scopus)


By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be nonunital, 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 isometrics. Every finite-dimensional 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 briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.

Original languageEnglish
Pages (from-to)437-456
Number of pages20
JournalLetters in Mathematical Physics
Issue number4
Publication statusPublished - jan. 1 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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