Geodesic
On nilpotent Lie algebras of derivations with large center
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 153-162 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\mathbb K$ be a field of characteristic zero and $A$ an associative commutative $\mathbb K$-algebra that is an integral domain. Denote by $R$ the quotient field of $A$ and by $W(A)=R\operatorname{Der} A$ the Lie algebra of derivations on $R$ that are products of elements of $R$ and derivations on $A$. Nilpotent Lie subalgebras of the Lie algebra $W(A)$ of rank $n$ over $R$ with the center of rank $n-1$ are studied. It is proved that such a Lie algebra $L$ is isomorphic to a subalgebra of the Lie algebra $u_n(F)$ of triangular polynomial derivations where $F$ is the field of constants for $L$.
Keywords: derivation, Lie algebra, triangular derivation
Mots-clés : nilpotent Lie subalgebra, polynomial algebra. 
@article{ADM_2016_21_1_a10,
     author = {Kateryna Sysak},
     title = {On nilpotent {Lie} algebras of derivations with large center},
     journal = {Algebra and discrete mathematics},
     pages = {153--162},
     year = {2016},
     volume = {21},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a10/}
}
TY  - JOUR
AU  - Kateryna Sysak
TI  - On nilpotent Lie algebras of derivations with large center
JO  - Algebra and discrete mathematics
PY  - 2016
SP  - 153
EP  - 162
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a10/
LA  - en
ID  - ADM_2016_21_1_a10
ER  - 
%0 Journal Article
%A Kateryna Sysak
%T On nilpotent Lie algebras of derivations with large center
%J Algebra and discrete mathematics
%D 2016
%P 153-162
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a10/
%G en
%F ADM_2016_21_1_a10
Kateryna Sysak. On nilpotent Lie algebras of derivations with large center. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 153-162. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a10/

[1] Yu. A. Bahturin, Identical Relations in Lie Algebras, Nauka, Moscow, 1985 (Russian)

[2] V. V. Bavula, “Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras”, Izv. RAN. Ser. Mat., 77:6 (2013), 3–44 | DOI | MR | Zbl

[3] V. V. Bavula, “The groups of automorphisms of the Lie algebras of triangular polynomial derivations”, J. Pure Appl. Algebra, 218:5 (2014), 829–851 | DOI | MR | Zbl

[4] J. Draisma, “Transitive Lie algebras of vector fields: an overview”, Qual. Theory Dyn. Syst., 11:1 (2012), 39–60 | DOI | MR | Zbl

[5] A. González-López, N. Kamran and P. J. Olver, “Lie algebras of differential operators in two complex variables”, Amer. J. Math., 114 (1992), 1163–1185 | DOI | MR | Zbl

[6] S. Lie, Theorie der Transformationsgruppen, v. 3, Leipzig, 1893

[7] Ie. O. Makedonskyi and A. P. Petravchuk, “On nilpotent and solvable Lie algebras of derivations”, Journal of Algebra, 401 (2014), 245–257 | DOI | MR | Zbl

[8] Ie. O. Makedonskyi and A. P. Petravchuk, “On finite dimensional Lie algebras of planar vector fields with rational coefficients”, Methods Func. Analysis Topology, 19:4 (2013), 376–388 | MR | Zbl