159 citations · 404 across the 61 of their papers we have counts for
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Algebraic groups generated by semisimple elements
Ivan Arzhantsev
Given a connected linear algebraic group over an algebraically closed field of characteristic zero, we describe the subgroup of generated by all semisimple elements.
Algebraic monoid structures on the affine 3-space
Ivan Arzhantsev, Roman Avdeev, Yulia Zaitseva
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also…
On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings
Ivan Arzhantsev, Sergey Gaifullin, Viktor Lopatkin
For a finite set of homogeneous locally nilpotent derivations of the algebra of polynomials in several variables, a finite dimensionality criterion for the Lie algebra generated by…
Affine cones as images of affine spaces
Ivan Arzhantsev
We prove that an affine cone admits a surjective morphism from an affine space if and only if is unirational.
On Normality of Projective Hypersurfaces with an Additive Action
Ivan Arzhantsev, Ivan Beldiev, Yulia Zaitseva
We study projective hypersurfaces admitting an induced additive action, i.e., an effective action of the vector group with an ope…
Uniqueness of addition in Lie algebras revisited
Ivan Arzhantsev
We obtain new and improve old results on uniqueness of addition in Lie rings and Lie algebras. A Lie ring is called a unique addition ring, or a UA-Lie ring, if any…