A constructive method to determine the variety of filiform Lie algebras
F. J. Echarte; M. C. Márquez; J. Núñez
Czechoslovak Mathematical Journal (2006)
- Volume: 56, Issue: 4, page 1281-1299
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topEcharte, F. J., Márquez, M. C., and Núñez, J.. "A constructive method to determine the variety of filiform Lie algebras." Czechoslovak Mathematical Journal 56.4 (2006): 1281-1299. <http://eudml.org/doc/31105>.
@article{Echarte2006,
abstract = {In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.},
author = {Echarte, F. J., Márquez, M. C., Núñez, J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {cohomology of nilpotent Lie algebras; graded filiform Lie algebras; variety of laws of filiform Lie algebras; irreducible component; algorithm; cohomology of nilpotent Lie algebras; graded filiform Lie algebras; variety of laws of filiform Lie algebras; irreducible component; algorithm},
language = {eng},
number = {4},
pages = {1281-1299},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A constructive method to determine the variety of filiform Lie algebras},
url = {http://eudml.org/doc/31105},
volume = {56},
year = {2006},
}
TY - JOUR
AU - Echarte, F. J.
AU - Márquez, M. C.
AU - Núñez, J.
TI - A constructive method to determine the variety of filiform Lie algebras
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1281
EP - 1299
AB - In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.
LA - eng
KW - cohomology of nilpotent Lie algebras; graded filiform Lie algebras; variety of laws of filiform Lie algebras; irreducible component; algorithm; cohomology of nilpotent Lie algebras; graded filiform Lie algebras; variety of laws of filiform Lie algebras; irreducible component; algorithm
UR - http://eudml.org/doc/31105
ER -
References
top- Cohomologie des algèbres de Lie nilpotentes. Application a l’étude de la variété des algèbres de Lie nilpotentes, Bull. Soc. Math. France 98 (1970), 81–116. (1970) Zbl0244.17011MR0289609
- 10.1007/BF02559602, Acta Math. 100 (1958), 45–92. (1958) Zbl0083.24802MR0102558DOI10.1007/BF02559602
- 10.1016/S0096-3003(99)00270-2, Applied Mathematics and Computation 121 (2001), 169–175. (2001) MR1830867DOI10.1016/S0096-3003(99)00270-2
- 10.1016/S1570-7954(00)80040-6, M. Hazewinkel (ed.), Elsevier, 2000. DOI10.1016/S1570-7954(00)80040-6
- Varieties of Lie Algebras Laws. Handbook of Algebra, Vol. 2, M. Hazewinkel (ed.), Elsevier, 2000.
- Nilpotent Lie Algebras, Kluwer Academic Publishers, , 1996. (1996) MR1383588
- Variété des lois d’algèbres de Lie nilpotentes, Geometriae Dedicata 40 (1991), 269–295. (1991) MR1137083
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.