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

Prince Koree Osei; Bernd Johannes Schroers

doi:10.1088/1361-6382/aaaa5e

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

Prince Koree Osei
, Bernd Johannes Schroers

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

169 Downloads (Pure)

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 some known r-matrices for special parameter values.

Original language	English
Article number	075006
Journal	Classical and Quantum Gravity
Volume	35
Issue number	7
Early online date	28 Feb 2018
DOIs	https://doi.org/10.1088/1361-6382/aaaa5e
Publication status	Published - 12 Apr 2018

Keywords

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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10.1088/1361-6382/aaaa5e

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This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://iopscience.iop.org/article/10.1088/1361-6382/aaaa5e/meta
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https://arxiv.org/abs/1708.07650

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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 some known r-matrices for special parameter values.",

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AB - 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.

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KW - Fock-Rosly Poisson structure

KW - Poisson-Lie structures

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ER -

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

Abstract

Keywords

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