{"paper":{"title":"Lifshitz symmetry: Lie algebras, spacetimes and particles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","gr-qc","math.DG"],"primary_cat":"hep-th","authors_text":"Jos\\'e Figueroa-O'Farrill, Ross Grassie, Stefan Prohazka","submitted_at":"2022-06-23T16:25:17Z","abstract_excerpt":"We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (\"particles\") of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name \"Lifshitz Lie algebras\". We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes:\n  (1) ($d+2$)-dimensional Lifs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11806","kind":"arxiv","version":3},"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/2206.11806/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"}