Affine structures on filiform Lie algebras

2005 ◽  
pp. 141-155 ◽  
Author(s):  
Yusupdjan Khakimdjanov
Keyword(s):  
Lie Algebras ◽  
Affine Structures ◽  
Filiform Lie Algebras

AFFINE STRUCTURES ON NILMANIFOLDS

1996 ◽  
Vol 07 (05) ◽  
pp. 599-616 ◽  
Author(s):  
DIETRICH BURDE
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Algebraic Variety ◽  
Lie Group ◽  
Affine Structure ◽  
Nilpotent Lie Algebra ◽  
Minimal Dimension ◽  
Affine Structures ◽  
Filiform Algebra ◽  
Filiform Lie Algebras

We investigate the existence of affine structures on nilmanifolds Γ\G in the case where the Lie algebra g of the Lie group G is filiform nilpotent of dimension less or equal to 11. Here we obtain examples of nilmanifolds without any affine structure in dimensions 10, 11. These are new counterexamples to the Milnor conjecture. So far examples in dimension 11 were known where the proof is complicated, see [5] and [4]. Using certain 2-cocycles we realize the filiform Lie algebras as deformation algebras from a standard graded filiform algebra. Thus we study the affine algebraic variety of complex filiform nilpotent Lie algebra structures of a given dimension ≤11. This approach simplifies the calculations, and the counterexamples in dimension 10 are less complicated than the known ones. We also obtain results for the minimal dimension µ(g) of a faithful g-module for these filiform Lie algebras g.

scholarly journals Links among Characteristically Nilpotent, $C$-Graded and Derived Filiform Lie Algebras

2005 ◽  
Vol 35 (4) ◽  
pp. 1081-1098
Author(s):  
J.C. Benjumea ◽  
F.J. Echarte ◽  
M.C. Márquez ◽  
J. Núñez
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

Family of p-Filiform Lie Algebras

1998 ◽  
pp. 93-102 ◽  
Author(s):  
J. M. Cabezas ◽  
J. R. Gómez ◽  
A. Jimenez-Merchán
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

On characteristically nilpotent filiform lie algebras of dimension 9

1995 ◽  
Vol 23 (8) ◽  
pp. 3059-3071 ◽  
Author(s):  
F.J. Castro-Jiménez ◽  
J. Núñez-Valdés
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

Expanding Automorphisms and Affine Structures on Nilpotent Lie Algebras with Few Generators

2003 ◽  
Vol 31 (12) ◽  
pp. 5847-5874
Author(s):  
Karel Dekimpe ◽  
Paul Igodt ◽  
Hannes Pouseele#
Keyword(s):  
Lie Algebras ◽  
Nilpotent Lie Algebras ◽  
Affine Structures

(n– 4)-filiform lie algebras

1999 ◽  
Vol 27 (10) ◽  
pp. 4803-4819 ◽  
Author(s):  
J.M. Cabezas ◽  
J.R. Gómez
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

scholarly journals Leibniz algebras associated with representations of filiform Lie algebras

2015 ◽  
Vol 98 ◽  
pp. 181-195 ◽  
Author(s):  
Sh.A. Ayupov ◽  
L.M. Camacho ◽  
A.Kh. Khudoyberdiyev ◽  
B.A. Omirov
Keyword(s):  
Lie Algebras ◽  
Leibniz Algebras ◽  
Filiform Lie Algebras
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