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arXiv · 0809.0052

Quantum double and $\kappa$-Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory

C. Meusburger
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Abstract

We review the role of Drinfeld doubles and kappa-Poincare symmetries in quantised (2+1)-gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and kappa-Poincare symmetries associated with the isometry groups of (2+1)-gravity. In particular, we explain that the usual kappa-Poincare symmetries with a timelike deformation are not directly associated with (2+1)-gravity. These kappa-Poincare symmetries are linked to Chern-Simons theory only in the de Sitter case, and the relevant Chern-Simons theory is physically inequivalent to (2+1)-gravity.

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BibTeXRIS

C. Meusburger. 2008-08-30. Quantum double and $\kappa$-Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory. https://doi.org/10.1139/p08-076

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