5 papers
The Lie algebra of polynomial vector fields on the affine space with constant divergence is -generated
Ivan Beldiev, Gleb Pogudin
A Lie algebra is said to be -generated if every nonzero element can be completed to a two-element generating set. We prove that the Lie algebra of polynomial vector fields wit…
Automorphism groups of non-normal rigid affine surfaces are finite-dimensional
Ivan Beldiev, Alexander Perepechko
It was recently established by Perepechko and Zaidenberg that the automorphism group of a normal affine surface is finite-dimensional if and only if the surface admits no non-trivi…
The Lie algebra of polynomial vector fields on the affine space is -generated
Ivan Beldiev
We prove that the infinite-dimensional Lie algebra of polynomial vector fields on the affine space $\KK^n$ is generated by two explicitly given elements.
On Picard Number and Dimension of Algebraic Homogeneous Spaces
Ivan Beldiev, Dmitry Timashev
An algebraic variety is called a homogeneous space if there exists a transitive regular action of an algebraic group on . We prove inequalities between the dimension of a ho…
The Group of Isometries of
Ivan Beldiev
We study the group of isometries of the Grothendieck group equipped with the standard Euler form defined by . We prov…