Lifshitz symmetry: Lie algebras, spacetimes and particles

Understand

We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits ("particles") of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator.

• As a first step we classify Lie algebras of this type in arbitrary dimension.
• Among them is the prototypical Lifshitz algebra, which motivates this work and the name "Lifshitz Lie algebras".
• We classify homogeneous spacetimes of Lifshitz Lie groups.