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

Understand

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 ${\rm ISL}(2,\mathbb{R})$ Kac-Moody group and the ${\rm BMS}_3$ group by including non-commutative supertranslations.
• The coadjoint representation in each case is defined, and the corresponding geometric actions on coadjoint orbits are presented.