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Journal Article

Galilean free Lie algebras

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

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1907.00410.pdf
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Citation

Gomis, J., Kleinschmidt, A., & Palmkvist, J. (2019). Galilean free Lie algebras. Journal of High Energy Physics, 2019(9): 109. doi:10.1007/JHEP09(2019)109.


Cite as: https://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.