The Schrödinger-Virasoro Algebra

As the first up-to-date, self-contained presentation of the recently discovered mathematical structure of the Schrödinger-Virasoro algebra, this monograph explains the key role this algebra of non-relativistic conformal symmetries plays in our interrogation of some models of non-equilibrium statistical physics. In the same way that Poincare invariance or conformal (Virasoro) invariance are central to our understanding of elementary particles, so the Schrödinger-Virasoro algebra are viewed as a vital element in the relevant field, and especially in recent developments pertaining to the non-relativistic AdS/CFT correspondence.
Exploring the structure of this infinite-dimensional Lie algebra leads the authors to touch on topics as varied as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry, as well as representation theory and the cohomology of infinite-dimensional Lie algebras, not to mention the spectral theory of Schrödinger operators.