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Journal of Applied Mathematics
Volume 2014, Article ID 173072, 12 pages
Research Article

Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9

1Department of Mechanical Engineering, University of La Rioja, 26004 Logroño, Spain
2Department of Applied Mathematics I, University of Sevilla, 41012 Seville, Spain
3Department of Electrical Engineering, University of La Rioja, 26004 Logroño, Spain

Received 3 November 2013; Accepted 2 January 2014; Published 6 March 2014

Academic Editor: Peter G. L. Leach

Copyright © 2014 Mercedes Pérez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.