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arXiv · 1708.07650

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

Prince K Osei·Bernd J Schroers
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Abstract

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 known solutions for special parameter values

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Prince K Osei, Bernd J Schroers. 2017-08-25. Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity. https://doi.org/10.1088/1361-6382%2Faaaa5e

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