相关论文: On Automorphisms of the Affine Cremona Group

Suppose $(X,\sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${\rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/\log^2 n)$, then ${\rm Aut}(X)$ is amenable (as a countable,…

In this paper, we discuss subgroups of the automorphism group of the polynomial ring in n variables over a field of characteristic zero. An automorphism F is said to be co-tame if the subgroup generated by F and affine automorphisms…

To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local…

We show that plane Cremona groups over finite fields embed as dense subgroups into Neretin groups, i.e. groups of almost automorphisms of rooted trees. We also show that if the finite base field has even characteristic and contains at least…

In this note we study the problem of characterizing the complex affine space $\mathbb{A}^n$ via its automorphism group. We prove the following. Let $X$ be an irreducible quasi-projective $n$-dimensional variety such that $\mathrm{Aut}(X)$…

A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as…

Using a filtration on the Grothendieck ring of triangulated categories, we define the categorical dimension of a birational map between smooth projective varieties. We show that birational automorphisms of bounded categorical dimension form…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of characteristic zero and some transformation groups of…

The Cremona group is topologically simple when endowed with the Zariski or Euclidean topology, in any dimension $\ge 2$ and over any infinite field. Two elements are moreover always connected by an affine line, so the group is…

It is well known that all Borel subgroups of a linear algebraic group are conjugate. This result also holds for the automorphism group ${{\mathrm{Aut}}} (\mathbb A^2)$ of the affine plane \cite{BerestEshmatovEshmatov2016} (see also…

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we…

Let $\Aut(G)$ denote the group of (bi-)continuous automorphisms %and $\Out(G)$ the outer automorphism group of a non-Archimedean Polish group~$G$. We show that for any such $G$ with an invariant countable basis of open subgroups, the group…

For a finitely generated free group F_n, of rank at least 2, any finite subgroup of Out(F_n) can be realized as a group of automorphisms of a graph with fundamental group F_n. This result, known as Out(F_n) realization, was proved by…

We prove that every biregular automorphism of the affine algebraic variety ${\mathbb P}^M\setminus S$, $M\geqslant 3$, where $S\subset {\mathbb P}^M$ is a hypersurface of degree $m\geqslant M+1$ with a unique singular point of multiplicity…

Let $\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\mathbb{F}_q$-automorphism group of $\mathcal{X}$ admits as an automorphism group the direct product of…

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the…

The automorphism groups ${\rm Aut\,}A_n$ and ${\rm Aut\,}W_n$ of the polynomial algebra $A_n=C[x_1,x_2,\cdots, x_n]$ and the rank $n$ Witt algebra $W_n={\rm Der\,}A_n$ are studied in this paper. It is well-known that ${\rm Aut\,}A_n$ for…

We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.