{"paper":{"title":"The Schr\\\"odinger-Virasoro Lie group and algebra: from geometry to representation theory","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Claude Roger, Jeremie Unterberger","submitted_at":"2006-01-24T17:46:01Z","abstract_excerpt":"This 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 Schr\\\"odinger equation and the central charge-free Virasoro algebra $Vect(S^1)$. We call $\\mathfrak{sv}$ the Schr\\\"odinger-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 s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0601050","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0601050/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}