The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements

Abstract

The Maxwell group in 2+1 dimensions is given by a particular extension of a semi-direct product. This mathematical structure provides a sound framework to study different generalizations of the Maxwell symmetry in three space-time dimensions. By giving a general definition of extended semi-direct products, we construct infinite-dimensional enhancements of the Maxwell group that enlarge the $\mathrm{ISL}(2,\mathbb{R})$ Kac-Moody group and the ${\mathrm{BMS}}_3$ group by including non-commutative supertranslations. The coadjoint representation in each case is defined, and the corresponding geometric actions on coadjoint orbits are presented. These actions lead to novel Wess-Zumino terms that naturally realize the aforementioned infinite-dimensional symmetries. We briefly elaborate on potential applications in the contexts of three-dimensional gravity, higher-spin symmetries, and quantum Hall systems.

42 pages, typos corrected

References in corpus (16)

• Topological Defects and Gapless Modes in Insulators and Superconductors
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Notes on the BMS group in three dimensions: I. Induced representations
• Expanding Lie (super)algebras through abelian semigroups
• Notes on the BMS group in three dimensions: II. Coadjoint representation
• Expansions of algebras and superalgebras and some applications
• Geometric actions for three-dimensional gravity
• Deformations of Maxwell algebra and their Dynamical Realizations
• Maxwell Superalgebras and Abelian Semigroup Expansion
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Generalized Poincare algebras and Lovelock-Cartan gravity theory
• Deformations of Maxwell Superalgebras and Their Applications
• BMS4 Algebra, Its Stability and Deformations
• On Rigidity of 3d Asymptotic Symmetry Algebras
• On the supersymmetry invariance of flat supergravity with boundary
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory

Cited by in corpus (10)

• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Three-dimensional Maxwellian extended Bargmann supergravity
• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Extended Kinematical 3D Gravity Theories
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• On Stabilization of Maxwell-BMS Algebra
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion