Geodesic
Complex Structures on Quasi-Filiform Lie Algebras
Lucia García Vergnolle1 ; Elizabeth Remm1, 2, 3, 4, 5
1Lab. de Mathématiques, Université de Haute Alsace, Faculté des Sciences et Techniques, 4 Rue des Frères Lumière, 68093 Mulhouse, France
2The aim of this article is to classify quasi-filiform nilpotent Lie algebras g, that is with nilindex dim g-2, admitting a complex structure. Note that the non-existence of complex structures over nilpotent Lie algebras of maximal class, also called filiform, has already been proved by M. Goze and E. Remm [Non existence of complex structures on filiform Lie algebras, Comm. Algebra 30 (2002) 3777--3788].
3Keywords: Complex structures, generalized complex structures, quasi-filiform Lie algebras.
4MSC: 17B60, 53C56, 17B60
5[
Journal of Lie Theory, Tome 19 (2009) no. 2, pp. 251-265

Voir la notice de l'article provenant de la source Heldermann Verlag

The aim of this article is to classify quasi-filiform nilpotent Lie algebras g, that is with nilindex dim g-2, admitting a complex structure. Note that the non-existence of complex structures over nilpotent Lie algebras of maximal class, also called filiform, has already been proved by M. Goze and E. Remm [Non existence of complex structures on filiform Lie algebras, Comm. Algebra 30 (2002) 3777--3788].
Classification : 17B60, 53C56, 17B60
Mots-clés : Complex structures, generalized complex structures, quasi-filiform Lie algebras

Lucia García Vergnolle  1   ; Elizabeth Remm  1 , 2 , 3 , 4 , 5

1 Lab. de Mathématiques, Université de Haute Alsace, Faculté des Sciences et Techniques, 4 Rue des Frères Lumière, 68093 Mulhouse, France
2 The aim of this article is to classify quasi-filiform nilpotent Lie algebras g, that is with nilindex dim g-2, admitting a complex structure. Note that the non-existence of complex structures over nilpotent Lie algebras of maximal class, also called filiform, has already been proved by M. Goze and E. Remm [Non existence of complex structures on filiform Lie algebras, Comm. Algebra 30 (2002) 3777--3788].
3 Keywords: Complex structures, generalized complex structures, quasi-filiform Lie algebras.
4 MSC: 17B60, 53C56, 17B60
5 [ 
Lucia García Vergnolle; Elizabeth Remm. Complex Structures on Quasi-Filiform Lie Algebras. Journal of Lie Theory, Tome 19 (2009) no. 2, pp. 251-265. http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a4/
@article{JOLT_2009_19_2_a4,
     author = {Lucia Garc{\'\i}a Vergnolle and Elizabeth Remm},
     title = {Complex {Structures} on {Quasi-Filiform} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {251--265},
     year = {2009},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_2_a4/}
}
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