{"paper":{"title":"Normed representations of weight quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.FA"],"primary_cat":"math.RT","authors_text":"Yu-Zhe Liu","submitted_at":"2025-07-09T15:49:07Z","abstract_excerpt":"Let $A$ and $B$ be two tensor rings given by weight quivers. We introduce norms for tensor rings and $(A,B)$-bimodules, and define an important category $\\mathscr{A}^p_{\\varsigma}$ in this paper whose object is a triple $(N,v,\\delta)$ given by an $(A,B)$-bimodule $N$, a special element $v\\in V$ satisfying some special conditions, and a special $(A,B)$-homomorphism $\\delta: N^{\\oplus_p 2^{\\dim A}} \\to N$ and each morphism $(N,v,\\delta) \\to (N',v',\\delta')$ is given by an $(A,B)$-homomorphism $\\theta: N\\to N'$ such that $\\theta(v)=v'$ and $\\delta' \\theta^{\\oplus 2^{\\dim A}} = \\theta\\delta$ hold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06962","kind":"arxiv","version":2},"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/2507.06962/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"}