A. P. Petravchuk

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Articles: 2

On finite dimensional Lie algebras of planar vector fields with rational coefficients

Methods Funct. Anal. Topology 19 (2013), no. 4, 376-388

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as subalgebras of this algebra.

On the group of Lie-orthogonal operators on a Lie algebra

Methods Funct. Anal. Topology 17 (2011), no. 3, 199-203

Finite dimensional Lie algebras over the field of complex numbers with a linear operator $T: L\to L$ such that $[T(x),T(y)]=[x,y]$ for all $x,y\in L$ are studied. The group of such non-degenerative linear operators on $L$ is considered. Some properties of this group and its relations with the group $\operatorname{Aut}(L)$ in the general linear group $GL(L)$ are described.