On generalizations of asymptotically AdS₃ spaces and geometry of SL(N)

In three and two dimensions the asymptotic symmetry groups of $AdS$ spaces are infinite dimensional. This can be explained easily by noting the relations $AdS_3 \simeq SL(2)$ and $AdS_2 \simeq SL(2)/SO(2)$, i.e. that the asymptotic symmetries are in fact that of the Lie group SL(2). As show in the author's previous work, similar infinite dimensional asymptotic symmetry groups can be found in the case of SL(3) and probably also for other noncompact Lie groups and their homogeneous spaces. The purpose of the present work is to revisit the $AdS_3$ space in detail from the Lie group point of view by finding the boundary theory energy-momentum tensor and to prepare to tackle the SL(3) and SL(N) cases.