{"paper":{"title":"Hochschild cohomology of relation extension algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, M. Andrea Gatica, Rachel Taillefer (LMBP), Ralf Schiffler","submitted_at":"2015-07-22T12:03:53Z","abstract_excerpt":"Let  $B$ be the split extension of a finite dimensional algebra $C$ by a $C$-$C$-bimodule $E$.  We define a morphism of associative graded algebras $\\varphi^*:\\HH^*(B)\\rightarrow \\HH^*(C)$ from the Hochschild cohomology of $B$ to that of $C$, extending similar constructions for the first cohomology groups made and studied by Assem, Bustamante, Igusa, Redondo and Schiffler. In the case of a trivial extension $B=C\\ltimes E$, we give necessary and sufficient conditions for each $\\varphi^n$ to be surjective.  We prove the surjectivity of $\\varphi^1$ for a class of trivial extensions that includes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06142","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"}