{"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/a-construction-of-einstein-solvmanifolds-not","title":"A construction of Einstein solvmanifolds not based on nilsolitons","arxiv_id":"2312.03125","date":"2023-12-05","proceeding":null,"authors":["Diego Conti","Federico A. Rossi","Romeo Segnan Dalmasso"],"abstract":"We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form $\\mathfrak{g}\\rtimes_D\\mathbb{R}$, where $\\mathfrak{g}$ is a nilpotent Lie algebra and $D$ is a nonsymmetric derivation. Considering nonsymmetric derivations has the consequence that $\\mathfrak{g}$ is not a nilsoliton, but satisfies a more general condition. Our construction is based on the notion of nondiagonal triple on a nice diagram. We present an algorithm to classify nondiagonal triples and the associated Einstein metrics. With the use of a computer, we obtain all solutions up to dimension $5$, and all solutions in dimension $\\leq9$ that satisfy an additional technical restriction. By comparing curvatures, we show that the Einstein solvmanifolds of dimension $\\leq 5$ that we obtain by our construction are not isometric to a standard extension of a nilsoliton.","url_abs":"https://arxiv.org/abs/2312.03125v3","url_pdf":"https://arxiv.org/pdf/2312.03125v3.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":"a-construction-of-einstein-solvmanifolds-not","repo_url":"https://github.com/diego-conti/jormungandr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}