Maximal solvable extensions of filiform algebras

Libor Šnobl

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 5, page 405-414
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Šnobl, Libor. "Maximal solvable extensions of filiform algebras." Archivum Mathematicum 047.5 (2011): 405-414. <http://eudml.org/doc/246506>.

@article{Šnobl2011,
abstract = {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.},
author = {Šnobl, Libor},
journal = {Archivum Mathematicum},
keywords = {solvable and nilpotent Lie algebras; filiform algebras; solvable Lie algebra; nilpotent Lie algebra; filiform algebra},
language = {eng},
number = {5},
pages = {405-414},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Maximal solvable extensions of filiform algebras},
url = {http://eudml.org/doc/246506},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Šnobl, Libor
TI - Maximal solvable extensions of filiform algebras
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 5
SP - 405
EP - 414
AB - 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.
LA - eng
KW - solvable and nilpotent Lie algebras; filiform algebras; solvable Lie algebra; nilpotent Lie algebra; filiform algebra
UR - http://eudml.org/doc/246506
ER -

References

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  1. Ancochea, J. M., Campoamor–Stursberg, R., Vergnolle, L. Garcia, 10.1088/0305-4470/39/6/008, J. Phys. A, Math. Theor. 39 (2006), 1339–1355. (2006) MR2202805DOI10.1088/0305-4470/39/6/008
  2. Campoamor–Stursberg, R., 10.1088/1751-8113/43/14/145202, J. Phys. A, Math. Theor. 43 (2010), Article ID 145202. (2010) MR2606433DOI10.1088/1751-8113/43/14/145202
  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. (1996) MR1600982
  4. Goze, M., Hakimjanov, Yu., 10.1007/BF02567448, Manuscripta Math. 84 (1994), 115–224. (1994) Zbl0823.17009MR1285951DOI10.1007/BF02567448
  5. Goze, M., Khakimdjanov, Yu., Nilpotent Lie algebras, Kluwer Academic Publishers Group, Dordrecht, 1996. (1996) Zbl0845.17012MR1383588
  6. Goze, M., Khakimdjanov, Yu., Handbook of algebra, vol. 2, ch. Nilpotent and solvable Lie algebras, pp. 615–663, North-Holland, Amsterdam, 2000. (2000) MR1759608
  7. Šnobl, L., 10.1088/1751-8113/43/50/505202, J. Phys. A, Math. Theor. 43 (2010), 17, Article ID 505202. (2010) Zbl1231.17004MR2740380DOI10.1088/1751-8113/43/50/505202
  8. Šnobl, L., Winternitz, P., 10.1088/0305-4470/38/12/011, J. Phys. A, Math. Theor. 38 (2005), 2687–2700. (2005) Zbl1063.22023MR2132082DOI10.1088/0305-4470/38/12/011
  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. (1968) Zbl0244.17010MR0245632

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