Quadratic 2-step Lie algebras: Computational algorithms and classification. (September 2019)

• Record Type: Journal Article
• Authors: Benito, Pilar; de-la-Concepción, Daniel; Roldán-López, Jorge; Sesma, Iciar
• Is Part Of: Journal of symbolic computation. Volume 94(2019)
• Page Start: 70
• Page End: 89
• Publication Date: 2019-09
• Subjects: 17B10 -- 17B30; Lie algebra -- Invariant bilinear form -- Nilpotent -- Free nilpotent -- Derivation -- Automorphism; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.07.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Taking into account the theoretical results and guidelines given in this work, we introduce a computational method to construct any 2-step nilpotent quadratic algebra of d generators. Along the work we show that the key of the classification of this class of metric algebras relies on certain families of skewsymmetric matrices. Computational examples for d ≤ 8 will be given.