Abstract
In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible Lie bialgebra structures and for selected examples we explicitely construct the related Hopf algebras. Using cohomological arguments we show that this construction can always be performed by a so-called twist deformation. The resulting structures can be compared to the well-known κ-Poincaré Hopf algebras constructed on the finite dimensional Poincaré or (anti) de Sitter algebra. The dual κ Minkowski spacetime is supposed to describe a specific non-commutative geometry. Importantly, we find that some incarnations of the κ-Poincaré can not be extended consistently to the infinite dimensional algebras. Furthermore, certain deformations can have potential physical applications if subalgebras are considered. Since the conserved charges associated with asymptotic symmetries in 3-dimensional form a centrally extended algebra we also discuss briefly deformations of such algebras. The presence of the full symmetry algebra might have observable consequences that could be used to rule out these deformations.
Highlights
Solution [11, 12], which makes 3-dimensional gravity a nice toy model for studying Hawking radiation
It was shown in this work that all Lie bialgebra structures on the symmetry algebra of asymptotically (A)dS spacetime in 3 dimensions are coboundary and triangular and can be quantized with the help of the Drinfeld twist technique
The triangularity condition constrains the possible Lie bialgebras and in particular some of the structures that are defined on the 3-dimensional Poincaré algebra related to κ-Poincaré quantum groups are eliminated due to this
Summary
We describe the structure of the Λ−BMS3 algebra of asymptotic symmetries. An extensive discussion of this algebra can be found in [45] and [46], which contain references to other works
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