Letters in Mathematical Physics

, Volume 38, Issue 4, pp 437–456

A coassociativeC*-quantum group with nonintegral dimensions

  • Gabriella Bòhm
  • Korníl Szlachónyi
Article

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.

Mathematics Subject Classification (1991)

81R50 

Key words

Weak Hopf algebras multiplicative isometries amalgamated crossed products 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

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

Personalised recommendations