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RESEARCH ARTICLE

On nilpotent Lie algebras of derivations with large center

Kateryna Sysak

Department of Algebra and Mathematical Logic, Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, 64, Volodymyrska street, 01033 Kyiv, Ukraine

Abstract: 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, nilpotent Lie subalgebra, triangular derivation, polynomial algebra.

MSC: Primary 17B66; Secondary 17B30, 13N15

Received: 24.12.2015
Revised: 10.02.2016

Language: English

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