{"paper":{"title":"Singular Hochschild Cohomology and Gerstenhaber Algebra Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Zhengfang Wang","submitted_at":"2015-08-02T04:26:49Z","abstract_excerpt":"In this paper, we define the singular Hochschild cohomology groups $HH_{sg}^i(A, A)$ of an associative $k$-algebra $A$ as morphisms from $A$ to $A[i]$ in the singular category $D_{sg}(A\\otimes_k A^{op})$ for $i\\in \\mathbb{Z}$. We prove that $HH_{sg}^*(A, A)$ has a Gerstenhaber algebra structure and in the case of a symmetric algebra $A$, $HH_{sg}^*(A, A)$ is a Batalin-Vilkovisky (BV) algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00190","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"}