| Title:
|
Maximal solvable extensions of filiform algebras (English) |
| Author:
|
Šnobl, Libor |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
405-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result. (English) |
| Keyword:
|
solvable and nilpotent Lie algebras |
| Keyword:
|
filiform algebras |
| MSC:
|
17B05 |
| MSC:
|
17B30 |
| MSC:
|
17B81 |
| idZBL:
|
Zbl 1265.17017 |
| idMR:
|
MR2876944 |
| . |
| Date available:
|
2011-12-16T15:29:16Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141788 |
| . |
| Reference:
|
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| Reference:
|
[2] Campoamor–Stursberg, R.: Solvable Lie algebras with an $\mathbb{N}$–graded nilradical of maximal nilpotency degree and their invariants.J. Phys. A, Math. Theor. 43 (2010), Article ID 145202. MR 2606433, 10.1088/1751-8113/43/14/145202 |
| Reference:
|
[3] Echarte, F. J., Gómez, J. R., Núñez, J.: Les algèbres de Lie filiformes complexes dérivées d’autres algèbres de Lie.[Complex filiform Lie algebras derived from other Lie algebras], Lois d'algèbres et variétés algébraiques (Colmar, 1991), Travaux en Cours 50, Hermann, Paris, 1996, pp. 45–55. MR 1600982 |
| Reference:
|
[4] Goze, M., Hakimjanov, Yu.: Sur les algèbres de Lie nilpotentes admettant un tore de derivations.Manuscripta Math. 84 (1994), 115–224. Zbl 0823.17009, MR 1285951, 10.1007/BF02567448 |
| Reference:
|
[5] Goze, M., Khakimdjanov, Yu.: Nilpotent Lie algebras.Kluwer Academic Publishers Group, Dordrecht, 1996. Zbl 0845.17012, MR 1383588 |
| Reference:
|
[6] Goze, M., Khakimdjanov, Yu.: Handbook of algebra.vol. 2, ch. Nilpotent and solvable Lie algebras, pp. 615–663, North-Holland, Amsterdam, 2000. MR 1759608 |
| Reference:
|
[7] Šnobl, L.: On the structure of maximal solvable extensions and of Levi extensions of nilpotent Lie algebras.J. Phys. A, Math. Theor. 43 (2010), 17, Article ID 505202. Zbl 1231.17004, MR 2740380, 10.1088/1751-8113/43/50/505202 |
| Reference:
|
[8] Šnobl, L., Winternitz, P.: A class of solvable Lie algebras and their Casimir invariants.J. Phys. A, Math. Theor. 38 (2005), 2687–2700. Zbl 1063.22023, MR 2132082, 10.1088/0305-4470/38/12/011 |
| Reference:
|
[9] Vergne, M.: Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes.C. R. Math. Acad. Sci. Paris Sèr. A–B 267 (1968), A867–A870. Zbl 0244.17010, MR 0245632 |
| . |
