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Elena I. Bunina

Publications and source records attributed to Elena I. Bunina.

8 recordsLinked to original sources
arXiv2026

Failure of direct finiteness for group algebras in every odd characteristic

For every odd prime $p$, we construct a finitely presented group $G_p$ and elements $a,b,c\in\mathbb{F}_p[G_p]$ such that $ab=1$, $ac=0$, and $c\ne0$. Thus $\mathbb{F}_p[G_p]$, and the group algebra over every field of characteristic $p$, fails to be directly finite. The construction combines a single exceptional self-product pair with signed bipartite cancellation. New integer matching data realize the exceptional self-intersection while retaining a strict squared-word decay estimate. We verify the adaptations needed for the earlier bounded-path and planar-localization arguments. A minimal disk picture protects the identity coefficient of $c$, so the proof does not require torsion-freeness.

math.GR↗
arXiv2026

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

We prove that all automorphisms of twisted Chevalley groups of type ${}^2D_\ell$, $\ell\ge4$, and their elementary subgroups over commutative local rings with $1/2$ are standard. More precisely, for elementary groups, every automorphism is a composition of strictly inner, diagonal, and ring automorphisms; for full groups, a central factor may also occur. In the adjoint case, diagonal automorphisms are strictly inner and the centre is trivial, so only strictly inner and ring factors are needed for both the elementary and full groups.

math.GR↗
arXiv2026

Automorphisms of twisted Chevalley groups of type ${}^2E_6$ over local rings

We classify abstract automorphisms of the elementary and full twisted Chevalley groups of type ${}^2E_6$ over commutative local rings with involution and $2$ invertible, for both isogeny types. Every automorphism is standard, with no invertibility assumption on $3$. In the adjoint case, it has a unique expression as a composition of conjugation by an element of the full twisted group and a ring automorphism commuting with the involution. For the simply connected form, the full group equals its elementary subgroup, and the factors are strictly inner, diagonal, and ring automorphisms. The main step replaces a linear change of basis by a group element. Invariant alternating tensors determine the transported Chevalley bracket. We correct this bracket over a faithfully flat local extension and descend the resulting conjugating element by uniqueness. Root-subgroup relations then recover the coefficient automorphism.

math.GR↗
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↗
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↗