From the 1 of 4 linked papers with an AI index.
4 papers
Non-cancellative varieties, maximal tori, and the Makar-Limanov invariant
Sergey Gaifullin, Mikhail Petrov
The paper constructs new counterexamples to the generalized Zariski cancellation problem and shows that the cylinders over these varieties have infinitely many non‑conjugate maxima…
Flexibility criterion for affine horospherical varieties
Sergey Gaifullin, Veronika Kikteva
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal ho…
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…
Modified Derksen invariant
Ilya Boldyrev, Sergey Gaifullin, Anton Shafarevich
Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locall…