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Title: Filiform Lie algebras of order 3

Abstract

The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

Authors:
 [1]
  1. Rosa María Navarro. Dpto. de Matemáticas, Universidad de Extremadura, Cáceres (Spain)
Publication Date:
OSTI Identifier:
22250774
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DEFORMATION; LIE GROUPS

Citation Formats

Navarro, R. M., E-mail: rnavarro@unex.es. Filiform Lie algebras of order 3. United States: N. p., 2014. Web. doi:10.1063/1.4869747.
Navarro, R. M., E-mail: rnavarro@unex.es. Filiform Lie algebras of order 3. United States. https://doi.org/10.1063/1.4869747
Navarro, R. M., E-mail: rnavarro@unex.es. 2014. "Filiform Lie algebras of order 3". United States. https://doi.org/10.1063/1.4869747.
@article{osti_22250774,
title = {Filiform Lie algebras of order 3},
author = {Navarro, R. M., E-mail: rnavarro@unex.es},
abstractNote = {The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.},
doi = {10.1063/1.4869747},
url = {https://www.osti.gov/biblio/22250774}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 4,
volume = 55,
place = {United States},
year = {Tue Apr 15 00:00:00 EDT 2014},
month = {Tue Apr 15 00:00:00 EDT 2014}
}