| Title:
|
A constructive method to determine the variety of filiform Lie algebras (English) |
| Author:
|
Echarte, F. J. |
| Author:
|
Márquez, M. C. |
| Author:
|
Núñez, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1281-1299 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
cohomology of nilpotent Lie algebras |
| Keyword:
|
graded filiform Lie algebras |
| Keyword:
|
variety of laws of filiform Lie algebras |
| Keyword:
|
irreducible component |
| Keyword:
|
algorithm |
| MSC:
|
17B30 |
| MSC:
|
17B56 |
| idZBL:
|
Zbl 1164.17012 |
| idMR:
|
MR2280809 |
| . |
| Date available:
|
2009-09-24T11:42:51Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128145 |
| . |
| Reference:
|
[1] M. Vergne: 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. Zbl 0244.17011, MR 0289609 |
| Reference:
|
[2] N. Blackburn: On a special class of $p$-groups.Acta Math. 100 (1958), 45–92. Zbl 0083.24802, MR 0102558, 10.1007/BF02559602 |
| Reference:
|
[3] L. Boza Prieto, E. M. Fedriani Martel, and J. Núñez Valdés: A new method for classifying complex filiform Lie algebras.Applied Mathematics and Computation 121 (2001), 169–175. MR 1830867, 10.1016/S0096-3003(99)00270-2 |
| Reference:
|
[4] M. Goze, Y. B. Khakimdjanov: Nilpotent and Solvable Lie Algebras. Handbook of Algebra, Vol. 2.M. Hazewinkel (ed.), Elsevier, 2000. 10.1016/S1570-7954(00)80040-6 |
| Reference:
|
[5] Y. B. Khakimdjanov: Varieties of Lie Algebras Laws. Handbook of Algebra, Vol. 2.M. Hazewinkel (ed.), Elsevier, 2000. |
| Reference:
|
[6] M. Goze, Y. B. Khakimdjanov: Nilpotent Lie Algebras.Kluwer Academic Publishers, , 1996. MR 1383588 |
| Reference:
|
[7] Y. B. Khakimdjanov: Variété des lois d’algèbres de Lie nilpotentes.Geometriae Dedicata 40 (1991), 269–295. MR 1137083 |
| . |
