Geodesic
On nilpotent Lie algebras of derivations with large center
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 153-162

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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. 
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     author = {Kateryna Sysak},
     title = {On nilpotent {Lie} algebras of derivations with large center},
     journal = {Algebra and discrete mathematics},
     pages = {153--162},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a10/}
}
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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/