相关论文: A note on Automorphisms of the Affine Cremona Grou…

We show that every automorphism of the group $\mathcal{G}_n:= \textrm{Aut}(\mathbb{A}^n)$ of polynomial automorphisms of complex affine $n$-space $\mathbb{A}^n=\mathbb{C}^n$ is inner up to field automorphisms when restricted to the subgroup…

Let $\overline G$ be the wonderful compactification of a simple affine algebraic group $G$ defined over $\mathbb C$ such that its center is trivial and $G\not= {\rm PSL}(2,\mathbb{C})$. Take a maximal torus $T \subset G$, and denote by…

We show that the automorphism group of affine n-space $A^n$ determines $A^n$ up to isomorphism: If $X$ is a connected affine variety such that $Aut(X)$ is isomorphic to $Aut(A^n)$ as ind-groups, then $X$ is isomorphic to $A^n$ as a variety.…

Let $\overline G$ be the wonderful compactification of a simple affine algebraic group $G$ of adjoint type defined over $\mathbb C.$ Let ${\overline T}\subset \overline G$ be the closure of a maximal torus $T\subset G.$ We prove that the…

A new infinite series of rational affine algebraic varieties is constructed whose automorphism group contains the automorphism group ${\rm Aut}(F_n)$ of the free group $F_n$ of rank $n$. The automorphism groups of such varieties are…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

We investigate the automorphism group of the quantised enveloping algebra U of the positive nilpotent part of certain simple complex Lie algebras g in the case where the deformation parameter q \in \mathbb{C}^* is not a root of unity.…

We prove the Andruskiewitsch-Dumas conjecture that the automorphism group of the positive part of the quantized universal enveloping algebra $U_q({\mathfrak{g}})$ of an arbitrary finite dimensional simple Lie algebra g is isomorphic to the…

In this paper we prove that if two normal affine surfaces $S$ and $S'$ have isomorphic automorphism groups, then every connected algebraic group acting regularly and faithfully on $S$ acts also regularly and faithfully on $S'$. Moreover, if…

A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type…

Given an affine algebraic variety $X$, we prove that if the neutral component $\mathrm{Aut}^\circ(X)$ of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves…

We prove two results about the natural representation of a group G of automorphisms of a normal projective threefold X on its second cohomology. We show that if X is minimal then G, modulo a normal subgroup of null entropy, is embedded as a…

Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $\lambda$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^\lambda)^T$ of the Schubert variety…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…

Let $G$ be a finite group and $M,N$ be two normal subgroups of $G$. Let $Aut_N^M(G)$ denote the group of all automorphisms of $G$ which fix $N$ element wise and act trivially on $G/M$. Let $n$ be a positive integer. In this article we have…

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define…

Let G be a group of automorphisms of a compact K\"ahler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

An element $g$ of a group $G$ is a test element if every endomorphism of $G$ that fixes $g$ is an automorphism. Let $G$ be a free group of finite rank, an orientable surface group of genus $n \geq 2$, or a non-orientable surface group of…

An automorphism $\alpha$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively…