{"paper":{"title":"Invariant theory and wheeled PROPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Harm Derksen, Visu Makam","submitted_at":"2019-09-01T18:32:34Z","abstract_excerpt":"We study the category of wheeled PROPs using tools from Invariant Theory. A typical example of a wheeled PROP is the mixed tensor algebra ${\\mathcal V}=T(V)\\otimes T(V^\\star)$, where $T(V)$ is the tensor algebra on an $n$-dimensional vector space over a field of $K$ of characteristic 0. First we classify all the ideals of the initial object ${\\mathcal{Z}}$ in the category of wheeled PROPs. We show that non-degenerate sub-wheeled PROPs of ${\\mathcal V}$ are exactly subalgebras of the form ${\\mathcal V}^G$ where $G$ is a closed, reductive subgroup of the general linear group ${\\rm GL}(V)$. When "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00443","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/1909.00443/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"}