The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical Schrödinger symmetries
Jérémie Unterberger, Claude Roger - The Schrödinger-Virasoro Algebra: Mathematical structure and dynamical Schrödinger symmetries
Published: 2011-10-26 | ISBN: 3642227163, 3642269591 | PDF | 260 pages | 3 MB
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 rôle 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 Schrödinger operators.