Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9. (6th March 2014)

• Record Type: Journal Article
• Authors: Pérez, Mercedes; Pérez, Francisco P.; Jiménez, Emilio
• Other Names: Leach Peter G. L. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-03-06
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/173072
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : On the basis of the family of quasifiliform Lie algebra laws of dimension 9 of 16 parameters and 17 constraints, this paper is devoted to identify the invariants that completely classify the algebras over the complex numbers except for isomorphism. It is proved that the nullification of certain parameters or of parameter expressions divides the family into subfamilies such that any couple of them is nonisomorphic and any quasifiliform Lie algebra of dimension 9 is isomorphic to one of them. The iterative and exhaustive computation with Maple provides the classification, which divides the original family into 263 subfamilies, composed of 157 simple algebras, 77 families depending on 1 parameter, 24 families depending on 2 parameters, and 5 families depending on 3 parameters.