Graded contractions of filiform Lie algebras

José M. Escobar; Juan Núñez Valdés; Pedro Pérez‐Fernández

doi:10.1002/mma.4785

Graded contractions of filiform Lie algebras

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4785 ◽

2018 ◽

Vol 41 (17) ◽

pp. 7195-7201

Author(s):

José M. Escobar ◽

Juan Núñez Valdés ◽

Pedro Pérez‐Fernández

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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

Rocky Mountain Journal of Mathematics ◽

10.1216/rmjm/1181069676 ◽

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

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Solvable infinite filiform Lie algebras

Journal of Commutative Algebra ◽

10.1216/jca-2010-2-4-429 ◽

2010 ◽

Vol 2 (4) ◽

pp. 429-436 ◽

Cited By ~ 2

Author(s):

Clas Löfwall

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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Family of p-Filiform Lie Algebras

Algebra and Operator Theory ◽

10.1007/978-94-011-5072-9_7 ◽

1998 ◽

pp. 93-102 ◽

Cited By ~ 9

Author(s):

J. M. Cabezas ◽

J. R. Gómez ◽

A. Jimenez-Merchán

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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On characteristically nilpotent filiform lie algebras of dimension 9

Communications in Algebra ◽

10.1080/00927879508825388 ◽

1995 ◽

Vol 23 (8) ◽

pp. 3059-3071 ◽

Cited By ~ 1

Author(s):

F.J. Castro-Jiménez ◽

J. Núñez-Valdés

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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(n– 4)-filiform lie algebras

Communications in Algebra ◽

10.1080/00927879908826731 ◽

1999 ◽

Vol 27 (10) ◽

pp. 4803-4819 ◽

Cited By ~ 4

Author(s):

J.M. Cabezas ◽

J.R. Gómez

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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Leibniz algebras associated with representations of filiform Lie algebras

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2015.08.002 ◽

2015 ◽

Vol 98 ◽

pp. 181-195 ◽

Cited By ~ 8

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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Affine structures on filiform Lie algebras

American Mathematical Society Translations: Series 2 - Lie Groups and Invariant Theory ◽

10.1090/trans2/213/09 ◽

2005 ◽

pp. 141-155 ◽

Cited By ~ 4

Author(s):

Yusupdjan Khakimdjanov

Keyword(s):

Lie Algebras ◽

Affine Structures ◽

Filiform Lie Algebras

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The cohomology of filiform Lie algebras of maximal rank

Linear Algebra and its Applications ◽

10.1016/j.laa.2014.04.031 ◽

2014 ◽

Vol 455 ◽

pp. 143-167

Author(s):

Leandro Cagliero ◽

Paulo Tirao

Keyword(s):

Lie Algebras ◽

Maximal Rank ◽

Filiform Lie Algebras

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Infinitesimal deformations of filiform Lie algebras of order 3

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2015.08.001 ◽

2015 ◽

Vol 98 ◽

pp. 150-159 ◽

Cited By ~ 3

Author(s):

R.M. Navarro

Keyword(s):

Lie Algebras ◽

Infinitesimal Deformations ◽

Filiform Lie Algebras

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FILIFORM LIE ALGEBRAS OF DIMENSION 8 AS DEGENERATIONS

Journal of Algebra and Its Applications ◽

10.1142/s0219498813501442 ◽

2014 ◽

Vol 13 (04) ◽

pp. 1350144 ◽

Cited By ~ 2

Author(s):

JOAN FELIPE HERRERA-GRANADA ◽

PAULO TIRAO

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Nilpotent Lie Algebras ◽

Filiform Lie Algebras ◽

Filiform Lie Algebra

For each complex 8-dimensional filiform Lie algebra we find another nonisomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank ≥ 1, only the characteristically nilpotent ones should be considered.

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