arXiv subjects

Elena I. Bunina

Publications and source records attributed to Elena I. Bunina.

6 recordsLinked to original sources

arXiv2026

Automorphisms of Twisted Chevalley Groups of type ${}^2 A_3$ and ${}^2 A_4$ over Local Rings

We give a complete classification of the automorphisms of twisted Chevalley groups of types ${}^2A_3$ and ${}^2A_4$, and of their elementary subgroups, over commutative local rings $R$ containing $1/2$ and equipped with a non-trivial involution $θ$. The classification covers all isogeny types and, together with our higher-rank result~\cite{EB&DM1}, completes the description for type ${}^2A_{\ell}$ with $\ell\geq3$.

math.GR↗

arXiv2026

Automorphisms of Twisted Chevalley Groups of type ${}^2 D_\ell \ (\ell \geq 4)$ over Local Rings

This paper is part of a series devoted to the classification of isomorphisms and automorphisms of twisted Chevalley groups over commutative rings. In this work, we prove that every automorphism of a twisted Chevalley group of type ${}^2 D_\ell$ ($\ell \geqslant 4$) over a local ring containing $1/2$ is standard.

math.GR↗

arXiv2026

Automorphisms of Twisted Chevalley Groups of type ${}^2 A_\ell \ (\ell \geq 5)$ over Local Rings

This paper is the first in a series devoted to the classification of automorphisms and isomorphisms of twisted Chevalley groups over commutative rings. In the present paper, we prove that every automorphism of a twisted Chevalley group of type ${}^2A_\ell$ $(\ell \geq 5)$ over a local ring in which $2$ is invertible is standard.

math.GR↗

arXiv2009

Automorphisms of Chevalley groups of type $B_l$ over local rings with 1/2

In the given paper we prove that every automorphism of a Chevalley group of type $B_l$, $l\geqslant 2$, over a commutative local ring with 1/2 is standard, i. e., it is a composition of ring, inner and central automorphisms.

math.GR↗

arXiv2006

Elementary equivalence of the semigroup of invertible matrices with nonnegative elements

In this paper, we prove that the semigroups of invertible matrices with nonnegative elements over linearly oredered associative rings are elementarily equivalent if and only if the matrices have the same dimension and the rings are elementarily equivalent as ordered rings.

math.RA↗

arXiv2006

Automorphisms of the semigroup of invertible matrices with nonnegative elements

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner automorphism of the semigroup, an automorphism of the ring preserving the order, and a central homothety.

math.RA↗