The Schrödinger-Virasoro algebra. Mathematical structure and dynamical Schrödinger symmetries.
Résumé
This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure -- the
Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key role in understanding, respectively,
elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected
to apply itself naturally to the study of some models on non-equilibrium statistical physics, or more specifically in the context of recent developments
related to the non-relativistic AdS/CFT correspondence.
The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras,
Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and
the spectral theory of Schrödinger operators.