Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity

Prince Koree Osei, Bernd Johannes Schroers

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6 Citations (Scopus)
81 Downloads (Pure)


We study the conditions for classical r-matrices to be compatible with the generalised Chern-Simons action for 3d gravity. Compatibility means solving the classical Yang-Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern-Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.

Original languageEnglish
Article number075006
JournalClassical and Quantum Gravity
Issue number7
Early online date28 Feb 2018
Publication statusPublished - 12 Apr 2018


  • 3d gravity
  • Chern-Simons theory
  • Classical Yang-Baxter equation
  • Fock-Rosly Poisson structure
  • Poisson-Lie structures

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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