Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9
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 para...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/173072 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |