The Schrödinger-Virasoro Lie group and algebra: from geometry to representation theory

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dc.creatorRoger, Claude
dc.creatorUnterberger, Jeremie
dc.date2006-01-24
dc.date.accessioned2026-07-07T07:51:05Z
dc.date.available2026-07-07T07:51:05Z
dc.descriptionThis article is concerned with an extensive study of an infinite-dimensional Lie algebra $\mathfrak{sv}$, introduced in the context of non-equilibrium statistical physics, containing as subalgebras both the Lie algebra of invariance of the free Schrödinger equation and the central charge-free Virasoro algebra $Vect(S^1)$. We call $\mathfrak{sv}$ the Schrödinger-Virasoro algebra. We choose to present $\mathfrak{sv}$ from a Newtonian geometry point of view first, and then in connection with conformal and Poisson geometry. We turn afterwards to its representation theory: realizations as Lie symmetries of field equations, coadjoint representation, coinduced representations in connection with Cartan's prolongation method (yielding analogues of the tensor density modules for $Vect(S^1)$), and finally Verma modules with a Kac determinant formula. We also present a detailed cohomological study, providing in particular a classification of deformations and central extensions; there appears a non-local cocycle.
dc.identifierhttps://arxiv.org/abs/math-ph/0601050
dc.identifierhttp://arxiv.org/abs/math-ph/0601050
dc.identifierAnn. Henri Poincare 7, 1477 (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125391
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subject17B55; 17B56; 17B63; 17B65; 17B66; 17B67; 17B68; 17B81; 22E65; 22E70; 82C10
dc.titleThe Schrödinger-Virasoro Lie group and algebra: from geometry to representation theory
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