3 papers
math.AC2026
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 $…
math.AG2026
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…
math.AG2025
Root monoids and active algebraic groups
Ekaterina Nistiuk, Yulia Zaitseva
We describe affine monoids whose group of invertible elements is an active semidirect product of a unipotent group and a torus, in terms of comultiplications on the algebra of regu…