{"paper":{"title":"Koszul properties of the moment map of some classical representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Aldo Conca, Hans-Christian Herbig, Srikanth B. Iyengar","submitted_at":"2017-05-07T19:48:48Z","abstract_excerpt":"This work concerns the moment map $\\mu$ associated with the standard representation of a classical Lie algebra. For applications to deformation quantization it is desirable that $S/(\\mu)$, the coordinate algebra of the zero fibre of $\\mu$, be Koszul. The main result is that this algebra is not Koszul for the standard representation of $\\mathfrak{sl}_{n}$, and of $\\mathfrak{sp}_{n}$. This is deduced from a computation of the Betti numbers of $S/(\\mu)$ as an $S$-module, which are of interest also from the point of view of commutative algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02688","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":""},"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"}