{"paper":{"title":"Lie Algebras of Derivations and Resolvent Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Detlev Buchholz, Hendrik Grundling","submitted_at":"2012-02-13T16:26:23Z","abstract_excerpt":"This paper analyzes the action {\\delta} of a Lie algebra X by derivations on a C*-algebra A. This action satisfies an \"almost inner\" property which ensures affiliation of the generators of the derivations {\\delta} with A, and is expressed in terms of corresponding pseudo-resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*-algebra A, it is shown that there is a central extension of X which determines algebraic relations of the underlying pseudo- resolvents. If the Lie action {\\delta} is ergodic, i.e. the only elements of A on which all the derivations in {\\delta}_x "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2780","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":""},"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"}