{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-certain-hochschild-cohomology-groups-for","title":"On certain Hochschild cohomology groups for the small quantum group","arxiv_id":"2104.05113","date":"2021-04-11","proceeding":null,"authors":["Nicolas Hemelsoet","Rik Voorhaar"],"abstract":"We apply the sheaf cohomology BGG method developed by the authors and Lachowska-Qi to the computation of Hochschild cohomology groups of various blocks of the small quantum group. All our computations of the center of the corresponding block agree with the conjectures of Lachowska-Qi. In the case of the nontrivial singular block for $\\mathfrak{g} = \\mathfrak{sl}_3$, we obtain the H*$(\\mathfrak{u}, \\mathbb{C}) = \\mathbb{C}[\\mathcal{N}]$-module structure of HH*$(\\mathfrak{u}_{\\lambda})$.","url_abs":"https://arxiv.org/abs/2104.05113v1","url_pdf":"https://arxiv.org/pdf/2104.05113v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-certain-hochschild-cohomology-groups-for","repo_url":"https://github.com/RikVoorhaar/bgg-cohomology","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}