46 citations · 147 across the 35 of their papers we have counts for
34 papers · 1 filter
Picard group of connected affine algebraic group
Vladimir L. Popov
We prove that the Picard group of a connected affine algebraic group is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathsc…
Faithful actions of automorphism groups of free groups on algebraic varieties
Vladimir L. Popov
Considering a certain construction of algebraic varieties endowed with an algebraic action of the group , , we obtain a criterion for the faithfulness…
Rationality of adjoint orbits
Vladimir L. Popov
We prove that every orbit of the adjoint representation of any connected reductive algebraic group is a rational algebraic variety. For complex simply connected semisimple ,…
Embeddings of groups into automorphism groups of algebraic varieties
Vladimir L. Popov
For every positive integer , we construct, using algebraic groups, an infinite family of irreducible algebraic varieties ,whose automorphism group contains the…
Underlying varieties and group structures
Vladimir L. Popov
We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.
On algebraic group varieties
Vladimir L. Popov
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.