Journal of Applied Mathematics

Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9

Mercedes Pérez, Francisco P. Pérez, and Emilio Jiménez

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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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 173072, 12 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305589

Digital Object Identifier
doi:10.1155/2014/173072

Mathematical Reviews number (MathSciNet)
MR3178951

Zentralblatt MATH identifier
07010560

Citation

Pérez, Mercedes; Pérez, Francisco P.; Jiménez, Emilio. Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9. J. Appl. Math. 2014 (2014), Article ID 173072, 12 pages. doi:10.1155/2014/173072. https://projecteuclid.org/euclid.jam/1425305589


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