A Coassociative C-Quantum Group with Nonintegral Dimensions

G. Böhm, Korníl Szlachónyi

Research output: Contribution to journalArticle

89 Citations (Scopus)

Abstract

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
Volume38
Issue number4
Publication statusPublished - 1996

Fingerprint

Quantum Groups
Hopf Algebra
algebra
Fusion Rule
fusion
antipodes
Antipode
Coproducts
Crossed Product
axioms
Isometric
Axioms
Multiplicative
Partial
Symmetry
symmetry
Arbitrary
products

Keywords

  • Amalgamated crossed products
  • Multiplicative isometrics
  • Weak Hopf algebras

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

A Coassociative C-Quantum Group with Nonintegral Dimensions. / Böhm, G.; Szlachónyi, Korníl.

In: Letters in Mathematical Physics, Vol. 38, No. 4, 1996, p. 437-456.

Research output: Contribution to journalArticle

Böhm, G. ; Szlachónyi, Korníl. / A Coassociative C-Quantum Group with Nonintegral Dimensions. In: Letters in Mathematical Physics. 1996 ; Vol. 38, No. 4. pp. 437-456.
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