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Extended kinematical 3D gravity theories
Dr. Concha-Aguilera, Patrick 
Facultad de Ingeniería 
Dra. Rodríguez-Durán, Evelyn 
Facultad de Ingeniería 
Pino, Daniel
Ravera, Lucrezia
10.1007/JHEP01(2024)040
Springer Nature
2024
In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the 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-defned 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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Chern-Simons theories
Gauge symmetry
Space-Time symmetries
Classical theories of gravity
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