{"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/digitalization-of-exceptional-simple-lie","title":"Digitalization of exceptional simple Lie algebras into matrices over complex numbers","arxiv_id":"2010.06696","date":"2020-10-01","proceeding":null,"authors":["Takao Imai"],"abstract":"We give the images of the adjoint representations of exceptional simple Lie algebras by matrices over complex numbers. Next, we digitalize these matrices by the use of Maxima, which is a computer algebra system. These digitalized matrices are provided by using Maxima's function. We prove that these digitalized matrices are closed by Lie bracket operations and make up simple Lie algebras. Moreover, to prove the type of the exceptional simple Lie algebra, we calculate the root system using Maxima for Lie bracket operations as matrix calculations. We show some examples of classical Lie subalgebras of these digitalized matrices.","url_abs":"https://arxiv.org/abs/2010.06696v3","url_pdf":"https://arxiv.org/pdf/2010.06696v3.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":"digitalization-of-exceptional-simple-lie","repo_url":"https://github.com/TakaoIMAI/An-example-of-e8","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}