Galilean free Lie algebras. (English) Zbl 1423.83056

Gomis, Joaquim; Kleinschmidt, Axel; Palmkvist, Jakob

J. High Energy Phys. 2019, No. 9, Paper No. 109, 21 p. (2019).

Summary: 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 of gravity and the objects that couple to them.

MSC:

81R10	Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
17B01	Identities, free Lie (super)algebras
17B67	Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
83D05	Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

Keywords:

generalized Newton-Cartan theories of gravity; space-time symmetries; classical theories of gravity; p-branes

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