{"paper":{"title":"Generalized derivations and general relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"L. Pysiak, M. Heller, T. Miller, W. Sasin","submitted_at":"2013-01-05T15:16:16Z","abstract_excerpt":"We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\\cal A} \\rightarrow {\\cal A}$ such that there exists a usual derivation $d$ of ${\\cal A}$ satisfying the generalized Leibniz rule $u(a b) = u(a) b + a \\, d(b)$ for all $a,b \\in \\cal A$. The generalized geometry \"is tested\" in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein-Hilbert action "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0910","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":""},"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"}