Abstract
In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the \( \mathfrak{so} \) (2, 2) algebra. We show that the Lie algebra expansion method based on semigroups reproduces not only the original kinematical algebras but also a family of non- and ultra-relativistic algebras. Remarkably, the extended kinematical algebras obtained as sequential expansions of the AdS algebra are characterized by a non-degenerate bilinear invariant form, ensuring the construction of a well-defined Chern-Simons gravity action in three spacetime dimensions. Contrary to the contraction process, the degeneracy of the non-Lorentzian theories is avoided without extending the relativistic algebra but considering a bigger semigroup. Using the properties of the expansion procedure, we show that our construction also applies at the level of the Chern-Simons action.
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Acknowledgments
This work was funded by the National Agency for Research and Development ANID — SIA grant No. SA77210097 and FONDECYT grants No. 1211077, 11220328 and 11220486. D.P. would like to thank to Universidad de Concepción, Chile, for Beca articulación pregrado-postgrado. L.R. would like to thank the DISAT of the Polytechnic of Turin and the INFN for financial support. P.C., L.R. and E.R. would like to thank to the Dirección de Investigación and Vice-rectoría de Investigación of the Universidad Católica de la Santísima Concepción, Chile, for their constant support. This work was supported by USC20102 Internacionalización Transversal en la UCSC: enfrentando los nuevos desafíos (P.C.).
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Concha, P., Pino, D., Ravera, L. et al. Extended kinematical 3D gravity theories. J. High Energ. Phys. 2024, 40 (2024). https://doi.org/10.1007/JHEP01(2024)040
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DOI: https://doi.org/10.1007/JHEP01(2024)040