{"paper":{"title":"Invariants of derived equivalences for admissible fractional Brauer graph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Admissible fractional Brauer graph algebras have combinatorial invariants preserved under derived equivalences.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bohan Xing","submitted_at":"2026-04-08T01:17:15Z","abstract_excerpt":"Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras can be viewed as repetitive algebras and $r$-fold trivial extensions of gentle algebras."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras can be viewed as repetitive algebras and r-fold trivial extensions of gentle algebras.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the newly defined class of admissible fractional Brauer graph algebras is sufficiently rich and that the proposed combinatorial invariants are indeed preserved under derived equivalences (requires explicit verification in the full text).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants for derived equivalences and can be realized as repetitive algebras and r-fold trivial extensions of gentle algebras.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Admissible fractional Brauer graph algebras have combinatorial invariants preserved under derived equivalences.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1192a37bec7f59d02281bb053f8afb79ad61595c9cd692eac628a4a3bc3383d2"},"source":{"id":"2604.06557","kind":"arxiv","version":2},"verdict":{"id":"22b0504d-6d63-4bd4-983d-ed9815dd696f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:36:42.531959Z","strongest_claim":"We study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras can be viewed as repetitive algebras and r-fold trivial extensions of gentle algebras.","one_line_summary":"Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants for derived equivalences and can be realized as repetitive algebras and r-fold trivial extensions of gentle algebras.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the newly defined class of admissible fractional Brauer graph algebras is sufficiently rich and that the proposed combinatorial invariants are indeed preserved under derived equivalences (requires explicit verification in the full text).","pith_extraction_headline":"Admissible fractional Brauer graph algebras have combinatorial invariants preserved under derived equivalences."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06557/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"}