{"paper":{"title":"On the first $\\tau$-tilting Hochschild cohomology of an algebra","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Andrea Solotar, Claude Cibils, Eduardo N. Marcos, Marcelo Lanzilotta","submitted_at":"2024-04-10T11:06:58Z","abstract_excerpt":"In this paper we introduce, according to one of the main ideas of $\\tau$-tilting theory, the $\\tau$-Hochschild cohomology in degree one of a finite dimensional $k$-algebra $\\Lambda$, where $k$ is a field. We define the excess of $\\Lambda$ as the difference between the dimensions of the $\\tau$-Hochschild cohomology in degree one and the dimension of the usual Hochschild cohomology in degree one.\n  One of the main results is that for a zero excess bound quiver algebra $\\Lambda=kQ/I$, the Hochschild cohomology in degree two $\\mathsf{HH}^2(\\Lambda) $ is isomorphic to the space of morphisms $\\maths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06916","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/2404.06916/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"}