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Galilean free Lie algebras

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1907.00410.pdf
(Preprint), 269KB

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Citation

Gomis, J., Kleinschmidt, A., & Palmkvist, J. (in preparation). Galilean free Lie algebras.


Cite as: http://hdl.handle.net/21.11116/0000-0003-F209-2
Abstract
We construct free Lie algebras which, together with the algebra of spatial rotations, form infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended non-relativistic objects and non-relativistic gravity theories. We show how various extensions of the ordinary Galilei algebra can be obtained by truncations and contractions, in some cases via an affine Kac-Moody algebra. The infinite-dimensional Lie algebras could be useful in the construction of generalized Newton-Cartan theories gravity theories and the objects that couple to them.