{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T16:33:37Z","timestamp":1725294817402},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]). This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n\u00d7n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.<\/jats:p>","DOI":"10.46298\/dmtcs.242","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T21:14:40Z","timestamp":1629753280000},"source":"Crossref","is-referenced-by-count":3,"title":["Computations in finite-dimensional Lie algebras"],"prefix":"10.46298","volume":"Vol. 1","author":[{"given":"A. M.","family":"Cohen","sequence":"first","affiliation":[{"name":"Department of mathematics and computing science [Eindhoven]"}]},{"given":"W. A.","family":"Graaf","sequence":"additional","affiliation":[{"name":"Department of mathematics and computing science [Eindhoven]"}]},{"given":"L.","family":"R\u00f3nyai","sequence":"additional","affiliation":[{"name":"Computer and Automation Research Institute [Budapest]"}]}],"member":"25203","published-online":{"date-parts":[[1997,1,1]]},"container-title":["Discrete Mathematics & Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dmtcs.episciences.org\/242\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dmtcs.episciences.org\/242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T19:31:38Z","timestamp":1687289498000},"score":1,"resource":{"primary":{"URL":"https:\/\/dmtcs.episciences.org\/242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1,1]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/dmtcs.242","relation":{"is-same-as":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-00955695v1","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1,1]]}}}