Galilean free Lie algebras

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.

arXiv comment22 pages. v2: Published version. Minor changes. References added

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Cited by in corpus (22)

• Non-Relativistic Gravity and its Coupling to Matter
• String Theory and String Newton-Cartan Geometry
• Relating non-relativistic string theories
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Oddity in nonrelativistic, strong gravity
• Symmetries of post-Galilean expansions
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Coset space actions for nonrelativistic strings
• Non-relativistic $k$-contractions of the Coadjoint Poincaré algebra
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Non-relativistic gravity theories in four spacetime dimensions
• Colourful Poincaré symmetry, gravity and particle actions
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Hydrodynamics in the Carrollian regime
• A free Lie algebra approach to curvature corrections to flat space-time
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Space-time Schrödinger symmetries of a post-Galilean particle