Geodesic
On the degenerations of finite dimensional nilpotent complex Leibniz algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 268-274 
I. S. Rakhimov. On the degenerations of finite dimensional nilpotent complex Leibniz algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 268-274. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a14/
@article{ZNSL_2005_321_a14,
     author = {I. S. Rakhimov},
     title = {On the degenerations of finite dimensional nilpotent complex {Leibniz} algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {268--274},
     year = {2005},
     volume = {321},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a14/}
}
TY  - JOUR
AU  - I. S. Rakhimov
TI  - On the degenerations of finite dimensional nilpotent complex Leibniz algebras
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 268
EP  - 274
VL  - 321
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a14/
LA  - en
ID  - ZNSL_2005_321_a14
ER  - 
%0 Journal Article
%A I. S. Rakhimov
%T On the degenerations of finite dimensional nilpotent complex Leibniz algebras
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 268-274
%V 321
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a14/
%G en
%F ZNSL_2005_321_a14

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the present paper a result on closedness of some families of finite-dimensional Leibniz algebras relatively to the Zarissky topology is obtained. Statements concerning degenerations of finite dimensional non-Lie nilpotent complex Leibniz algebras are proved.

[1] P. Gabriel, “Finite representation type is open”, Proceedings of ICRA, I (Ottawa, 1974), Lect. Notes Math., 488, Springer-Verlag, 1975, 132–155 | MR

[2] G. Mazzola, “The algebraic and geometric classification of associative algebras of dimension five”, Manuscripta Math., 27 (1979), 1–21 | DOI | MR

[3] F. Grunewald, J. O'Halloran, “Varieties of nilpotent Lie algebras of dimension less than six”, J. Algebra, 112:2 (1988), 315–326 | DOI | MR

[4] D. Burde, C. Steinhoff, “Classification of orbit closures of $4$-dimensional complex Lie algebras”, J. Algebra, 214 (1999), 729–739 | DOI | MR | Zbl

[5] M. Goze M., J. M. Ancochea Bermudez, “On the varieties of nilpotent Lie algebras of dimension $7$ and $8$”, J. Pure Appl. Algebra, 77 (1992), 131–140 | DOI | MR | Zbl

[6] J.-L. Loday, “Une version non commutative des alg$\grave{e}$bres de Lie: les alg$\grave{e}$bres de Leibniz”, Ens. Math., 39 (1993), 269–293 | MR | Zbl

[7] Sh. A. Ayupov, B. A. Omirov, “On some classes of nilpotent Leibniz algebras”, Siberian Math. J., 42:1 (2001), 18–29 | DOI | MR | Zbl