Stable tameness of automorphisms of F<x,y,z> fixing z

On the lifting of the Nagata automorphism

It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra $F[x,y,z]$ over a field $F$ cannot be lifted to a $z$-automorphism ($z$-coordinate, respectively) of the free associative algebra $K<x,y,z>$. The proof is based on the following two new results which have their own interests: degree estimate of ${Q*_FF<x_1,...,x_n>}$ and tameness of the automorphism group ${\text{Aut}_Q(Q*_FF<x,y>)}$.

Tame Automorphisms Fixing a Variable of Free Associative Algebras of Rank Three

We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix the variable z. We describe the structure of the group of z-tame automorphisms and derive algorithms which recognize z-tame automorphisms and z-tame coordinates.

Automorphisms fixing a variable of K<x,y,z>

We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix z and such that the images of x, y are linear with respect to x, y. We prove that some of these automorphisms are wild in the class of all automorphisms fixing z, including the well known automorphism discovered by Anick, and show how to recognize the wild ones. This class of automorphisms induces tame automorphisms of the polynomial algebra K[x,y,z]. For n>2 the automorphisms of K<x_1,...,x_n,z> which fix z and are linear in the x's are tame.

自由双交换交换代数的Chein自同构

Chein Automorphisms of Free Metabelian Anticommutative Algebras

本文研究了自由双交换交换代数中只移动一个变量的Chein自同构，证明了当秩为2时自同构是线性的，并指出度数为3的Chein自同构在n≥3时具有绝对野性。

Leavitt 路径代数的自同构：Zhang 扭转与不可约表示

Automorphisms of Leavitt path algebras: Zhang twist and irreducible representations

本文通过角上的广义线性群构造任意图 Leavitt 路径代数固定顶点的自同构，并借此研究 Zhang 扭转及玫瑰图 R_n 的新不可约表示。

Universal enveloping algebras and universal derivations of Poisson algebras

Let $k$ be an arbitrary field of characteristic $0$. It is shown that for any $n\geq 1$ the universal enveloping algebras of the Poisson symplectic algebra $P_n(k)$ and the Weyl algebra $A_n(k)$ are isomorphic and the canonical isomorphism between them easily leads to the Moyal product. A basis of the universal enveloping algebra $P^e$ of a free Poisson algebra $P=k\{x_1,...,x_n\}$ is constructed and proved that the left dependency of a finite number of elements of $P^e$ over $P^e$ is algorithmically recognizable. We prove that if two elements of a free Poisson algebra do not generate a free t…