相关论文: The Anick automorphism of free associative algebra…

In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a Z-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that can not be…

We describe all automorphisms of a free metabelian anticommutative algebra of rank $n\geq 3$ over a field $K$ that move only one variable while fixing the others. Such automorphisms are called Chein automorphisms in the cases of free…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

We study so called weakly-periodic twisted-multiplicative automorphisms of the free skew-field. In particular, we show that any automorphism of a free skew-field that is defined by a periodic automorphism of a free group is equivalent to a…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups…

Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F)…

We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are…

In one of our recent papers, the associative and the Lie algebras of Weyl type $A[D]=A\otimes F[D]$ were defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of any characteristic,…

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism.

An algebra with identities $(a,b,c)=(a,c,b)=(b,a,c)$ is called {\it assosymmetric}, where $(x,y,z)=(xy)z-x(yz)$ is associator. We study $S_n$-module, $A_n$-module and $GL_n$-module structures of free assosymmetric algebra.

The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.

An automorphism of a compact complex space is called wild in the sense of Reichstein--Rogalski--Zhang if there is no non-trivial proper invariant analytic subset. We show that a compact complex surface admitting a wild automorphism must be…

We give a criterion of tameness and wildness for a finite-dimensional Lie algebra over an algebraically closed field.

For $N\geq 4$, we show that there exist automorphisms of the free group $F_N$ which have a parabolic orbit in $\partial F_N$. In fact, we exhibit a technology for producing infinitely many such examples.

We prove the Freiheitssatz for Novikov algebras in characteristic zero. It is also proved that the variety of Novikov algebras is generated by a Novikov algebra on the space of polynomials $k[x]$ in a single variable $x$ over a field $k$…

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of $\C^3$ is not closed, when the latter…

We prove that every derivation and every locally nilpotent derivation of the subalgebra $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$, where $n\geq 2$, of the polynomial algebra $K[x,y]$ in two variables over a field $K$ of characteristic zero is…

We prove that if a field k is infinite, char(k)=0 and k has not nontrivial automorphisms then automorphic equivalence of representations of Lie algebras coincide with geometric equivalence. We achieve our result by consideration of 1-sorted…

We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a proof of the tameness of automorphisms for two generated free Poisson algebras and prove that an analogue of the commutator test theorem is equivalent to…