10 papers
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.
Infinite transitivity and polynomial vector fields
Rafael B. Andrist, Ivan Arzhantsev
We prove that for many pairs of root subgroups of the automorphism group the diagonal action of the group generated by on $(\mathbb…
Borel subalgebras of Lie algebras of vector fields
Ivan Arzhantsev, Mikhail Zaidenberg
In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solv…
Elements of finite order in the normalizer of a maximal torus of a semisimple group
Ivan Arzhantsev, Alexey Galt, Alexey Staroletov
We prove that the set of elements of a given finite order in the connected component of the normalizer of a maximal torus of a semisimple group is either emp…
On flexibility of affine factorial varieties
Ivan Arzhantsev, Kirill Shakhmatov
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine fact…
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…