On the semiduals of local isometry groups in three-dimensional gravity

Prince Koree Osei, Bernd Johannes Schroers

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this way we obtain quantum doubles of the Lorentz and rotation groups in 3d, as well as kappa-Poincare algebras whose associated r-matrices have spacelike, timelike and lightlike deformation parameters. We confirm and elaborate the interpretation of semiduality proposed in [13] as the exchange of the cosmological length scale and the Planck mass in the context of 3d quantum gravity. In particular, semiduality gives a simple understanding of why the quantum double of the Lorentz group and the kappa-Poincare algebra with spacelike deformation parameter are both associated to 3d gravity with vanishing cosmological constant, while the kappa-Poincare algebra with a timelike deformation parameter can only be associated to 3d gravity if one takes the Planck mass to be imaginary.
Original languageEnglish
Pages (from-to)073510
Number of pages26
JournalJournal of Mathematical Physics
Volume53
Issue number7
DOIs
Publication statusPublished - Jul 2012

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