Classical r-matrices via semidualisation

Prince Koree Osei, Bernd Johannes Schroers

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3 Citations (Scopus)

Abstract

We study the interplay between double cross sum decompositions of a given Lie algebra and classical r-matrices for its semidual. For a class of Lie algebras which can be obtained by a process of generalised complexification we derive an expression for classical r-matrices of the semidual Lie bialgebra in terms of the data which determines the decomposition of the original Lie algebra. Applied to the local isometry Lie algebras arising in three-dimensional gravity, decomposition, and semidualisation yields the main class of non-trivial r-matrices for the Euclidean and Poincare group in three dimensions. In addition, the construction links the r-matrices with the Bianchi classification of three-dimensional real Lie algebras. (C) 2013 AIP Publishing LLC.

Original languageEnglish
Article number101702
Number of pages17
JournalJournal of Mathematical Physics
Volume54
Issue number10
DOIs
Publication statusPublished - Oct 2013

Keywords

  • QUANTUM POINCARE ALGEBRA
  • 3 DIMENSIONS
  • RELATIVITY
  • GRAVITY

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