Publication: On 2-abelian (n-5)-filiform Lie algebras
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2001
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Marcel Dekker
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Abstract
We classify the (n − 5)-filiform Lie algebras which have the additional property of a non-abelian derived subalgebra. Moreover we show that if a (n − 5)-filiform Lie algebra is characteristically nilpotent, then it must be 2-abelian.
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1. Ancochea, J.M. On The Rigidity of Solvable Lie Algebras, ASI NATO
Serie C247 (1986), 4037445.
2. Ancochea, J.M.; Campoamor, O.R. On Lie Algebras whose Nilradical
is (np)-filiform. Communications in Algebra (to appear).by [ ] at 02:58 16 March 2012
ORDER REPRINTS
3. Bratzlavsky, F. Sur les Alge`bres Admettant Un Tore Des De´rivations
Donne´ . J. of Algebra 1974, 30, 3057316.
4. Cabezas, J.M.; Go´ mez, J.R.; Jime´nez-Mercha´ n, A. A Family of
p-filiform Lie Algebras, Algebra and Operator Theory. Proceedings of
the Colloquium in Tashkent 1997, 937102.
5. Carles, R. Sur Les Alge`bres De Lie Caracte´ristiquement Nilpotentes;
Preprint Univ.: Poitiers, 1984.
6. Cerezo, A. Les alge`bres De Lie Nilpotentes Re´ eles Et Complexes De
Dimension 6. Publ. Univ. Nice 1983, 27.
7. Dixmier, J.; Lister, W.G. Derivations of Nilpotent Lie Algebras. Proc.
Amer. Math. Soc. 1957, 8, 1557158.
8. Dixmier, J. Cohomologie Des Alge`bres De Lie Nilpotentes. Acta Sci.
Mat. Szeged 1955, 16, 2467250.
9. Dyer, J.L. A Nilpotent Lie Algebra with Unipotent Automorphism
Group. Bull. Amer. Math. Soc. 1970, 52756.
10. Favre, G. Une Alge`bre De Lie Caracte´ristiquement Nilpotente De
Dimension 7. C. R. A. Sci. Paris 1972, 274, 133871339.
11. Favre, G. Syste`me Des Poids Sur Une Alge`bre De Lie Nilpotente.
Manuscripta Math. 1973, 9, 53790.
12. Go´ mez, J.R.; Goze, M.; Khakimdjanov, Yu.B. On the k-Abelian
Filiform Lie Algebras. Communications in Algebra 1997, 25 (2),
4317450.
13. Goze, M. Perturbations Sur Une Varie´te´ Alge´brique: Application a`
l’e´tude de la Varie´ te´ Des Lois d’alge`bre de Lie sur Cn, C. R. A. Sci.
Paris 1982, 295, 5837586.
14. Goze, M. E´ tude Locale de la Varie´ te´ des lois d’alge`bres de Lie. The` se,
1982, Mulhouse.
15. Goze. M. Crite`res Cohomologiques Pour la Rigidite´ de lois Algebriques.
Bull. Soc. Math. Belgique, 1991, XLIII 33742.
16. Goze,M.; Khakimdjanov, Yu.B. Sur les Alge`bres de Lie Admettant un
Tore de De´rivations. Manuscripta Math. 1994, 84, 1157124.
17. Goze, M.; Khakimdjanov, Yu.B. Alge`bres de Lie nilpotentes; Kluwer
Acad. Press: 1996.
18. Grunewald, F. O’Halloran, J. Varieties of Nilpotent Lie Algebras of
Dimensions Less Than Six. J. of Algebra 1990, 18 (10), 3157325.
19. Jacobson, N. A Note on Automorphisms and Derivations of Lie
Algebras. Proc. Amer. Math. Soc. 1955, 6, 2817283.
20. Khakimdjanov, Yu.B. Characteristically Nilpotent Lie Algebras.
Math. USSR Sbornik 1991, 70 (1).
21. Leger, O.; Toˆgoˆ . S. Characteristically Nilpotent Lie Algebras. Duke
Math. J. 1959, 26, 6237628.22. Leger, G.; Luks, E. On Derivations and Holomorphs of Nilpotent Lie
Algebras. Nagoya Math. J. 1971, 44, 39750.
23. Leger, G.; Luks. E. On a Duality for Metabelian Lie algebras.
J. of Algebra 1972, 21, 2667270.
24. Luks, E. What is the Typical Nilpotent Lie Algebra, in Computers in
Nonassociative Rings and Algebras; Academic Press: 1977.
25. Morozov, V.V. Classification des Alge`bres de Lie Nilpotentes de
Dimension 6, Izv. Vyssh. Ucheb. Zar 1958, 4, 1617171.
26. Mostov, G.D. Fully Reductible Subgroups of Algebraic Groups.
Amer. J. Math. 1956, 78.
27. Seeley, C. Some Nilpotent Lie Algebras of Even Dimension. Bull.
Austral. Math. Soc. 1992, 45, 71777.
28. Toˆgoˆ , S. On the Derivation Algebras of Lie Algebras. Canadian
J. Math. 1961, 13 (2), 2017216.
29. Toˆgoˆ , S. Outer Derivations of Lie Algebras. Trans. Amer. Math. Soc.
1967, 128, 2647276.
30. Vergne, M. Varie´te´ des Alge`bres de Lie Nilpotentes, The´ se. Paris 1966.
31. Vergne, M. Cohomologie des Alge`bres de Lie Nilpotentes. Application
a` l’e´tude de la Varle´te´ des Aige`bres de Lie Nilpotentes. Bull. Soc.
Math. France 1970, 98, 817116.
32. Yamaguchi, S. Derivations and Affine Structures of Some Nilpotent
Lie Algebras. Mem. Fac. Sci Kyushu Univ. Ser. 1980, A 34, 1517170.