Bicovariant differential calculus on quantum groups SUq(N) and SOq(N)

Ursula Carow-Watamura, Michael Schlieker, Satoshi Watamura, Wolfgang Weich

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)

Abstract

Following Woronowicz's proposal the bicovariant differential calculus on the quantum groups SUq(N) and SOq(N) is constructed. A systematic construction of bicovariant bimodules by using the {Mathematical expression} matrix is presented. The relation between the Hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules, and the q-deformed universal enveloping algebras is given. Imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined. As an application the Maurer-Cartan equations and the q-analogue of the structure constants are formulated.

Original languageEnglish
Pages (from-to)605-641
Number of pages37
JournalCommunications in Mathematical Physics
Volume142
Issue number3
DOIs
Publication statusPublished - 1991 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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