The Schr?dinger-Virasoro Algebra: Mathematical Structure and Dynamical Schr?dinger Symmetries

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure--the Schr?dinger-Virasoro algebra. Just as Poincar? invariance or conformal (Virasoro) invariance play a key r?le 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 of 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 Schr?dinger operators.