BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

TL;DR

This paper explores the structure and quantum deformations of BMS symmetries in 3 and 4 dimensions, revealing infinite subalgebras and constructing various Hopf algebra deformations, which may inform quantum spacetime models.

Contribution

It identifies multiple Poincaré subalgebras within BMS algebras and constructs numerous quantum deformations, including twist-deformations and duals, advancing understanding of quantum symmetries.

Findings

Infinite Poincaré subalgebras in BMS algebras

Construction of multiple Hopf algebra deformations

Discussion of noncommutative quantum spacetimes

Abstract

BMS symmetry is a symmetry of asymptotically flat spacetimes in the vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincar\'e subalgebras, a fact that has previously been noted in the 3-dimensional case only. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.