{"paper":{"title":"$L_\\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"L∞-algebraic central extensions of kinematical Lie algebras produce towers of p-form fields for brane couplings.","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Hyungrok Kim","submitted_at":"2025-12-07T17:49:43Z","abstract_excerpt":"The Newtonian limit of Newton-Cartan gravity relies crucially on the Lie-algebraic central extension to the Galilean algebra, namely the Bargmann algebra. Lie-algebraic central extensions naturally generalise to $L_\\infty$-algebraic central extensions, which in turn classify branes in superstring theory via the brane bouquet. This paper classifies all $L_\\infty$-algebraic central extensions of all kinematical Lie algebras that do not depend on the spatial rotation generators as well as all iterated central extensions thereof (for codimensions $\\le3$). The Bargmann central extension of the Gali"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The sequence of L_∞-algebraic central extensions in each degree then corresponds to a tower of p-form fields. After imposing conventional constraints, the zero-form field provides absolute time, and the higher-form fields are certain wedge products of the field strengths of the one-form (Bargmann) gravitational field.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That conventional constraints can be imposed on the L_infinity cocycles so that the resulting p-form fields remain consistent with the non-Lorentzian gravity equations and produce well-defined brane couplings without introducing new inconsistencies.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"L_infinity extensions of Galilean, Newton-Hooke and static algebras produce infinite towers of p-form fields that couple to torsionful non-Lorentzian gravities and yield WZW terms for (p-1)-branes via doubled coordinates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"L∞-algebraic central extensions of kinematical Lie algebras produce towers of p-form fields for brane couplings.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8427f4369999ece53fb2e8625a17964cb50073dbcd8b118ee50a942daf29b607"},"source":{"id":"2512.06942","kind":"arxiv","version":2},"verdict":{"id":"199f5693-5e13-4f10-95d0-6a2923db35c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T00:16:58.283051Z","strongest_claim":"The sequence of L_∞-algebraic central extensions in each degree then corresponds to a tower of p-form fields. After imposing conventional constraints, the zero-form field provides absolute time, and the higher-form fields are certain wedge products of the field strengths of the one-form (Bargmann) gravitational field.","one_line_summary":"L_infinity extensions of Galilean, Newton-Hooke and static algebras produce infinite towers of p-form fields that couple to torsionful non-Lorentzian gravities and yield WZW terms for (p-1)-branes via doubled coordinates.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That conventional constraints can be imposed on the L_infinity cocycles so that the resulting p-form fields remain consistent with the non-Lorentzian gravity equations and produce well-defined brane couplings without introducing new inconsistencies.","pith_extraction_headline":"L∞-algebraic central extensions of kinematical Lie algebras produce towers of p-form fields for brane couplings."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.06942/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":70,"sample":[{"doi":"10.3389/fphy.2023.1116888","year":2023,"title":"Review on non-relativistic gravity.Frontiers in Physics, 11:1116888, March 2023.arXiv: 2212.11309,doi:10.3389/fphy.2023.1116888","work_id":"914d3e33-79c1-4844-abb1-30af0ab84fac","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.21468/scipostphyslectnotes.69","year":2023,"title":"A non-lorentzian primer.SciPost Physics Lecture Notes, 69:1, May 2023","work_id":"0b173d59-7c94-4820-aa40-a3ebfbfb63c9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-981-19-3079-9_52-1","year":2023,"title":"Non-Lorentzian supergravity","work_id":"5ab22df3-4303-4650-a845-56a6a920c260","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.difgeo.2022.101894","year":2022,"title":"Non-lorentzian spacetimes.Differential Geometry and its Applications, 82:101894, June 2022.arXiv:2204.13609, doi:10.1016/j.difgeo.2022.101894","work_id":"47b84a53-ef64-406a-9451-89dea8c996f7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited","work_id":"d696d3d7-8297-457e-8bf4-191217ef72fd","ref_index":5,"cited_arxiv_id":"0909.2617","is_internal_anchor":true}],"resolved_work":70,"snapshot_sha256":"71f776ddcee410622a33b3f85e86a119cc46bc4f9244dbd5a7c07639c5519849","internal_anchors":35},"formal_canon":{"evidence_count":2,"snapshot_sha256":"327095f537cd19a339af2850d6b76cc9e59a218363c233aaa9e5bc354762b009"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}