Coadjoint Representation of the Schrödinger–Virasoro Group

2011 ◽  
pp. 31-42
Author(s):  
Jérémie Unterberger ◽  
Claude Roger
Keyword(s):  
Coadjoint Representation ◽  
Virasoro Group

scholarly journals Loop variables and the Virasoro group

1993 ◽  
Vol 405 (2-3) ◽  
pp. 367-388 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Virasoro Group

scholarly journals Higher-order polarizations on the Virasoro group and anomalies

1991 ◽  
Vol 139 (3) ◽  
pp. 433-440 ◽  
Author(s):  
Victor Aldaya ◽  
Jose Navarro-Salas
Keyword(s):  
Higher Order ◽  
Virasoro Group

scholarly journals BMS flux algebra in celestial holography

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Laura Donnay ◽  
Romain Ruzziconi
Keyword(s):  
Solution Space ◽  
Coadjoint Representation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Stress Energy ◽  
Momentum Fluxes ◽  
Non Local ◽  
Asymptotic Symmetries

Abstract Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

From Diffeomorphisms to Dark Energy?

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2467-2474 ◽  
Author(s):  
Vincent G. J. Rodgers ◽  
Takeshi Yasuda
Keyword(s):  
Dark Energy ◽  
Lie Algebras ◽  
Virasoro Algebra ◽  
Two Dimensions ◽  
Coadjoint Orbits ◽  
Coadjoint Representation ◽  
Natural Setting ◽  
Affine Lie Algebras ◽  
Yang Mills ◽  
Geometric Action

There are two physical actions that have a natural setting in terms of the coadjoint representation of the algebra of diffeomorphisms and of affine Lie algebras. One is the usual geometric action that comes from coadjoint orbits. The other action lives on the phase space that is transverse to the orbits and are called transverse actions, where Yang-Mills theory in two dimensions is an example. Here we show that the transverse action associated with the Virasoro algebra might contain clues for a theory for dark energy. These actions might also suggests a mechanism for symmetry changing.

EXTENDED BOTT–VIRASORO ALGEBRA, SEMIDIRECT PRODUCT, ⋆-LIE ALGEBRA OF DIFFEOMORPHISM AND NONCOMMUTATIVE INTEGRABLE SYSTEMS

2009 ◽  
Vol 06 (04) ◽  
pp. 555-572
Author(s):  
PARTHA GUHA
Keyword(s):  
Lie Algebra ◽  
Semidirect Product ◽  
Virasoro Algebra ◽  
Lie Derivative ◽  
Coadjoint Representation ◽  
Kdv Equations ◽  
Two Component ◽  
Universal Extension ◽  
Product Algebra ◽  
Tensor Densities

We study noncommutative theory of a coadjoint representation of a universal extension of Vect (S1) ⋉ C∞(S1) algebra using the action of ⋆-deformed matrix Hill's operators Δ⋆ on the space of ⋆-deformed tensor densities. The centrally extended semidirect product algebra [Formula: see text] is a Lie algebra of extended semidirect product of the Bott–Virasoro group [Formula: see text]. The study of deformed diffeomorphisms, deformed semidirect product algebra and deformed Lie derivative action of Δ⋆ on ⋆ deformed tensor-densities on S1 allow us to construct noncommutative two component Korteweg–de Vries (KdV) equations, in particular, we derive the noncommutative Ito equation. This leads to a geometric formulation of ⋆-deformed quantization of the centrally extended semidirect product algebra [Formula: see text] and two component noncommutative KdV equations.

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