Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity
High Energy Physics - Theory
2018-04-04 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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
Keywords
Cite
@article{arxiv.1708.07650,
title = {Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity},
author = {Prince K Osei and Bernd J Schroers},
journal= {arXiv preprint arXiv:1708.07650},
year = {2018}
}
Comments
20 pages, minor corrections and comments added in v2