E. Voronetsky

activity

20192026

K_{1}

6 citations · 29 across the 20 of their papers we have counts for

collaborators

21 papers

math.KT2026

Solvability of isotropic $K_{1}$ -functor over semilocal rings

Egor Voronetsky

We show that the $K_{1}$ -functor modeled on simple reductive groups over semilocal rings is solvable if the isotropic rank is at least $2$ and that the Tits index is nei…

math.RT2026

Nilpotency of locally isotropic $K_{1}$ -functor

Egor Voronetsky

We show that the $K_{1}$ -functor modeled on locally isotropic reductive groups is hypoabelian if the base ring has finite Bass--Serre dimension and, for the Tits index $ \…

math.RT2026

Weyl elements in isotropic reductive groups

Egor Voronetsky

We study Weyl elements in isotropic reductive groups over commutative rings. Our main result in an explicit formula for squares of such elements. We also classify these elements in…

math.GR2025

Locally isotropic Steinberg groups II. Schur multipliers

Egor Voronetsky

We compute Schur multipliers of locally isotropic Steinberg groups and of all root graded Steinberg groups with root systems of rank at least $3$ (excluding the types $ \mathsf H…

math.NT2025

The Diophantine problem in isotropic reductive groups

Egor Voronetsky

We begin to study model-theoretic properties of non-split isotropic reductive group schemes. In this paper we show that the base ring $K$ is e-interpretable in the point group $G(K…

math.RT2024

Locally isotropic Steinberg groups I. Centrality of the $K_{2}$ -functor

Egor Voronetsky

We begin to study Steinberg groups associated with a locally isotropic reductive group $G$ over a arbitrary ring. We propose a construction of such a Steinberg group functor as a g…

math.GR2024

Root graded groups revisited

Egor Voronetsky

A group $G$ is called root graded if it has a family of subgroups $G_{α}$ indexed by roots from a root system $Φ$ satisfying natural conditions similar to Chevalley groups over commu…

math.GR2023★ 1 cited

Locally isotropic elementary groups

Egor Voronetsky

We construct elementary subgroups of all reductive groups of the local isotropic rank $\geq 2$ over rings and prove their basic properties. In particular, our results may be applie…

math.GR2023

Groups with $BC_{ℓ}$ -commutator relations

Egor Voronetsky

Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root…

math.GR2023

Cosheaves of Steinberg pro-groups

Egor Voronetsky

Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with g…

math.GR2022

A presentation of relative unitary Steinberg groups

Egor Voronetsky

We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. t…

math.GR2022

Actions of pro-groups and pro-rings

Egor Voronetsky

We give an explicit description of internal actions in the semi-abelian categories of pro-groups and non-unital pro-rings in terms of actions of group objects and ring objects in $…

math.GR2022★ 1 cited

Groups with $A_{ℓ}$ -commutator relations

Egor Voronetsky

If $A$ is a unital associative ring and $ℓ \geq 2$ , then the general linear group $GL (ℓ, A)$ has root subgroups $U_{α}$ and Weyl elements $n_{α}$ for $α$ from the root s…

math.GR2021★ 3 cited

On the $A^{1}$ -invariance of $K_{2}$ modeled on linear and even orthogonal groups

Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky

Let $k$ be an arbitrary field. In this paper we show that in the linear case ( $Φ = A_{ℓ}$ , $ℓ \geq 4$ ) and even orthogonal case ( $Φ = D_{ℓ}$ , $ℓ \geq 7$ , $\ma…

math.GR2021★ 4 cited

Explicit presentation of relative Steinberg groups

Egor Voronetsky

We find an explicit presentation of relative linear Steinberg groups $St (n, R, I)$ for any ring $R$ and $n \geq 4$ by generators and relations as abstract groups. We also…

math.GR2020

Another presentation of orthogonal Steinberg groups

Egor Voronetsky

We use the pro-group approach to show that $StO (M, q)$ admits van der Kallen's "another presentation", where $M$ is a module over a commutative ring with sufficiently isot…

math.GR2020★ 4 cited

Centrality of $K_{2}$ for Chevalley groups: a pro-group approach

Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky

We prove the centrality of $K_{2} (F_{4}, R)$ for an arbitrary commutative ring $R$ . This completes the proof of the centrality of $K_{2} (Φ, R)$ for any roo…

math.GR2020★ 2 cited

Centrality of odd unitary $K_{2}$ -functor

Egor Voronetsky

Let $(R, Δ)$ be an odd form algebra. We show that the unitary Steinberg group $StU (R, Δ)$ is a crossed module over the odd unitary group $U (R, Δ)$ in two major cas…

math.GR2020★ 3 cited

Twisted forms of classical groups

Egor Voronetsky

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some excep…

math.GR2019★ 6 cited

Stability for odd unitary $K_{1}$

Egor Voronetsky

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_{1}$ -functor without using…

math.GR2019★ 5 cited

Groups normalized by the odd unitary group

Egor Voronetsky

We will give a definition of quadratic forms on bimodules and prove the sandwich classification theorem for subgroups of the general linear group $GL (P)$ normalized by the…

Solvability of isotropic K1​-functor over semilocal rings

Nilpotency of locally isotropic K1​-functor

Weyl elements in isotropic reductive groups

Locally isotropic Steinberg groups II. Schur multipliers

The Diophantine problem in isotropic reductive groups

Locally isotropic Steinberg groups I. Centrality of the K2​-functor

Root graded groups revisited

Locally isotropic elementary groups

Groups with BCℓ​-commutator relations

Cosheaves of Steinberg pro-groups

A presentation of relative unitary Steinberg groups

Actions of pro-groups and pro-rings

Groups with Aℓ​-commutator relations

On the A1-invariance of K2​ modeled on linear and even orthogonal groups

Explicit presentation of relative Steinberg groups

Another presentation of orthogonal Steinberg groups

Centrality of K2​ for Chevalley groups: a pro-group approach

Centrality of odd unitary K2​-functor

Twisted forms of classical groups

Stability for odd unitary K1​

Groups normalized by the odd unitary group

Solvability of isotropic $K_{1}$ -functor over semilocal rings

Nilpotency of locally isotropic $K_{1}$ -functor

Locally isotropic Steinberg groups I. Centrality of the $K_{2}$ -functor

Groups with $BC_{ℓ}$ -commutator relations

Groups with $A_{ℓ}$ -commutator relations

On the $A^{1}$ -invariance of $K_{2}$ modeled on linear and even orthogonal groups

Centrality of $K_{2}$ for Chevalley groups: a pro-group approach

Centrality of odd unitary $K_{2}$ -functor

Stability for odd unitary $K_{1}$