2 citations · 2 across the 5 of their papers we have counts for
5 papers
An infinite series of Gorenstein local algebras failing the affine homogeneity property
Roman Avdeev, Yulia Zaitseva
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras for . We give an elementary proof that the maximal ideal of every algebra $…
Connecting orbits in quasiaffine spherical varieties via -root subgroups
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group with a Borel subgroup and a quasiaffine spherical -variety , we prove that every -orbit contained in the regular lo…
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…
Root subgroups on horospherical varieties
Roman Avdeev, Vladimir Zhgoon
Given a connected reductive algebraic group and a spherical -variety , a -root subgroup on is a one-parameter additive group of automorphisms of normalized by…
On the existence of -root subgroups on affine spherical varieties
Roman Avdeev, Vladimir Zhgoon
Let be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group . In this paper we provide sufficient conditions, f…