Maxwell kinematical algebras and 3D gravities

Abstract

In this paper, we present a Maxwell extension of kinematical Lie algebras by promoting the contraction method underlying the Bacry and Lévy-Leblond cube to a semigroup expansion framework. Within this approach, we show that both non- and ultra-relativistic Maxwell algebras admitting non-degenerate invariant bilinear forms can be systematically obtained from different parent algebras through a unified expansion scheme, leading to a Maxwellian kinematical cube. This construction is further generalized to an infinite hierarchy of kinematical algebras. The expansion method naturally provides the corresponding invariant tensors, allowing for the systematic construction of three-dimensional Chern-Simons gravity theories.

Figures (4)

• Figure 1: Bacry and Lévy-Leblond cube of kinematical algebras Bacry:1968zf.
• Figure 2: Extended kinematical algebras starting from the AdS algebra Concha:2023bly.
• Figure 3: Maxwellian generalization of the extended kinematical algebras.
• Figure 4: $\mathfrak{B}_k$ generalization of the extended kinematical algebras.