{"paper":{"title":"Self-injective Jacobian algebras from Postnikov diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrea Pasquali","submitted_at":"2017-06-27T09:48:19Z","abstract_excerpt":"We study a finite-dimensional algebra $\\Lambda$ constructed from a Postnikov diagram $D$ in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent. Thus $\\Lambda$ is isomorphic to the stable endomorphism algebra of the cluster tilting module $T\\in\\underline{\\operatorname{CM}}(B)$ introduced by Jensen-King-Su in order to categorify the cluster algebra structure of $\\mathbb C[\\operatorname{Gr}_k(\\mathbb C^n)]$. We show that $\\Lambda$ is self-injective if and only if $D$ has a certain rotational symmetry. In this case, $\\Lambda$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08756","kind":"arxiv","version":4},"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"}