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Poisson brackets and two-generated subalgebras of rings of polynomials

- I. Shestakov, U. Umirbaev
- Mathematics
- 3 October 2003

Let A = F [x1, x2, . . . , xn] be a ring of polynomials over a field F on the variables x1, x2, . . . , xn. It is well known (see, for example, [11]) that the study of automorphisms of the algebra A… Expand

The tame and the wild automorphisms of polynomial rings in three variables

- I. Shestakov, U. Umirbaev
- Mathematics
- 3 October 2003

Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism τ ∈… Expand

An envelope for Malcev algebras

- J. M. Pérez-Izquierdo, I. Shestakov
- Mathematics
- 1 February 2004

We prove that for every Malcev algebra M there exist an algebra U(M) and a monomorphism ι:M→U(M)− of M into the commutator algebra U(M)− such that the image of M lies into the alternative center of… Expand

Free Akivis Algebras, Primitive Elements, and Hyperalgebras

- I. Shestakov, U. Umirbaev
- Mathematics
- 15 April 2002

Free Akivis algebras and primitive elements in their universal enveloping algebras are investigated. It is proved that subalgebras of free Akivis algebras are free and that finitely generated… Expand

Gradings on simple Jordan and Lie algebras

- Y. Bahturin, I. Shestakov, M. Zaicev
- Mathematics
- 15 January 2005

Abstract In this paper we describe all group gradings by a finite Abelian group G of several types of simple Jordan and Lie algebras over an algebraically closed field F of characteristic zero.

The Nagata automorphism is wild

- I. Shestakov, U. Umirbaev
- Mathematics, Medicine
- Proceedings of the National Academy of Sciences…
- 20 October 2003

It is proved that the well known Nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild, that is, it can not be decomposed into a product of… Expand

PBW-Pairs of Varieties of Linear Algebras

- A. Mikhalev, I. Shestakov
- Mathematics
- 1 February 2014

The notion of a Poincaré–Birkhoff–Witt (PBW)-pair of varieties of linear algebras over a field is under consideration. Examples of PBW-pairs are given. We prove that if (𝒱, 𝒲) is a PBW-pair and the… Expand

Quantization of Poisson Superalgebras and Speciality of Jordan Poisson Superalgebras

- I. Shestakov
- Mathematics
- 1994

The problem of speciality and i-speciality is considered for Jordan superalgebras related with Poisson superalgebras. The quantizations of Poisson superalgebras play an important role in the… Expand

Speciality of Malcev superalgebras on one odd generator

- I. Shestakov, N. Zhukavets
- Mathematics
- 15 July 2006

It is proved that every Malcev superalgebra generated by an odd element is special, that is, isomorphic to a subsuperalgebra of the commutator Malcev superalgebra A− for a certain alternative… Expand

Polynomial Identities of Finite Dimensional Simple Algebras

- I. Shestakov, M. Zaicev
- Mathematics
- 16 March 2011

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

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