{"paper":{"title":"Universal deformation rings for a class of self-injective special biserial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hernan Giraldo, Johny Calderon-Henao, Jose A. Velez-Marulanda, Ricardo Rueda-Robayo","submitted_at":"2016-05-31T17:59:49Z","abstract_excerpt":"Let $\\mathbf{k}$ be an algebraically closed field of arbitrary characteristic, let $\\Lambda$ be a finite dimensional $\\mathbf{k}$-algebra and let $V$ be a $\\Lambda$-module with stable endomorphism ring isomorphic to $\\mathbf{k}$. If $\\Lambda$ is self-injective, then $V$ has a universal deformation ring $R(\\Lambda,V)$, which is a complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$. Moreover, if $\\Lambda$ is further a Frobenius $\\mathbf{k}$-algebra, then $R(\\Lambda,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09746","kind":"arxiv","version":3},"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"}