{"paper":{"title":"Graded Naimark's Problem for Leavitt Path Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ashish K Srivastava, Kulumani M. Rangaswamy","submitted_at":"2025-06-10T00:31:48Z","abstract_excerpt":"In this paper we study the graded version of Naimark's problem for Leavitt path algebras considering them as $\\mathbb{Z}$-graded algebras. Several characterizations are obtained of a Leavitt path algebra $L$ of an arbitrary graph $E$ over a field $\\mathbb{K}$ over which any two graded-simple modules are graded isomorphic. Such a Leavitt path algebra $L$ is shown to be graded isomorphic to the algebra of graded infinite matrices having at most finitely many non-zero entries from the ring $R$ where $R=\\mathbb{K}$ or $R=\\mathbb{K}[x,x^{-1}]$. Equivalently, $L$ is a graded-simple ring which is gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08305","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/2506.08305/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"}