Classification of the quasifiliform nilpotent lie algebras of dimension 9

  1. Pérez, M. 2
  2. Pérez, F.P. 1
  3. Jiménez, E. 2
  1. 1 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Applied Mathematics

ISSN: 1110-757X

Año de publicación: 2014

Volumen: 2014

Tipo: Artículo

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DOI: 10.1155/2014/173072 SCOPUS: 2-s2.0-84896907182 WoS: WOS:000332970400001 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Journal of Applied Mathematics

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Resumen

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. © 2014 Mercedes Pérez et al.