Contractions from Grading

Abstract

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically, via identifying appropriate ${\mathbb{Z}}_m$-gradings (and their generalizations) on the parent algebra. This includes various types of flat space/Carroll limits of finite and infinite dimensional (A)dS algebras, as well as Galilean and Galilean Conformal algebras. Our observations can be regarded as providing a natural context for the Grassmann approach of arXiv:1312.2941. We also introduce a related notion, which we call partial grading, that arises naturally in this context.

v1:18 pages, v2:Refs added, minor improvements

References in corpus (10)

• Galilean Conformal Algebras and AdS/CFT
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Flat space (higher spin) gravity with chemical potentials
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• Spectral Flow in 3D Flat Spacetimes
• Low Tension Strings on a Cosmological Singularity
• On the dynamical symmetric algebra of ageing: Lie structure, representations and Appell systems