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Poisson brackets and two-generated subalgebras of rings of polynomials
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 AExpand
The tame and the wild automorphisms of polynomial rings in three variables
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
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 ofExpand
Free Akivis Algebras, Primitive Elements, and Hyperalgebras
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 generatedExpand
Gradings on simple Jordan and Lie algebras
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
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 ofExpand
PBW-Pairs of Varieties of Linear Algebras
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 theExpand
Quantization of Poisson Superalgebras and Speciality of Jordan Poisson Superalgebras
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 theExpand
Speciality of Malcev superalgebras on one odd generator
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 alternativeExpand
Polynomial Identities of Finite Dimensional Simple Algebras
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.