On deformations and extensions of Diff(S.sup.2./sup.)

0552333 - FZÚ 2022 RIV US eng J - Journal Article
Rojo, M.E. - Procházka, Tomáš - Sachs, I.
On deformations and extensions of Diff(S²).
Journal of High Energy Physics. Roč. 2021, č. 10 (2021), č. článku 133. ISSN 1029-8479. E-ISSN 1029-8479
R&D Projects: GA ČR(CZ) GX20-25775X
Institutional support: RVO:68378271
Keywords : representations * algebras * space-time symmetries * cassical theories of gravity * conformal and W symmetry * gauge-gravity correspondence
OECD category: Particles and field physics
Impact factor: 6.376, year: 2021
Method of publishing: Open access

We investigate the algebra of vector fields on the sphere. First, we find that linear deformations of this algebra are obstructed under reasonable conditions. In particular, we show that hs[λ], the one-parameter deformation of the algebra of area-preserving vector fields, does not extend to the entire algebra. Next, we study some non-central extensions through the embedding of vect mathfrak{vect} vect(S2^{2}2) into vect mathfrak{vect} vect(ℂ∗^{*}∗). For the latter, we discuss a three parameter family of non-central extensions which contains the symmetry algebra of asymptotically flat and asymptotically Friedmann spacetimes at future null infinity, admitting a simple free field realization.
Permanent Link: http://hdl.handle.net/11104/0327474