{"paper":{"title":"Universal deformation rings of string modules over a certain symmetric special biserial algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2012-12-23T02:36:35Z","abstract_excerpt":"Let $\\k$ be an algebraically closed field, let $\\A$ be a finite dimensional $\\k$-algebra and let $V$ be a $\\A$-module with stable endomorphism ring isomorphic to $\\k$. If $\\A$ is self-injective then $V$ has a universal deformation ring $R(\\A,V)$, which is a complete local commutative Noetherian $\\k$-algebra with residue field $\\k$. Moreover, if $\\Lambda$ is also a Frobenius $\\k$-algebra then $R(\\A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $\\Ar$-modules whose stable endomorphism ring isomorphic to $\\k$, where $\\Ar$ is a symmetric spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5754","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":""},"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"}