Related papers: On the Constant Reductions of Automorphism Groups …

Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$), ${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an $F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We fix a Haar…

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…

We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant…

It is proved that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups.

We derive precise formulas for the archimedean Euler factors occurring in certain standard Langlands $L$-functions for unitary groups. In the 1980s, Paul Garrett, as well as Ilya Piatetski-Shapiro and Stephen Rallis (independently of…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest are the components of the `partition vector' of the theory. These constitute an…

This paper studies automorphisms and monomorphisms of direct products $\Gamma=\Gamma_1\times\cdots\times\Gamma_r$ of finitely generated virtually solvable minimax groups, a class containing all virtually polycyclic groups. Under an…

We introduce a class of automorphisms of rooted $d$-regular trees arising from affine actions on their boundaries viewed as infinite dimensional vector spaces. This class includes, in particular, many examples of self-similar realizations…

In the 1970s Stallings showed that one could learn a great deal about free groups and their automorphisms by viewing the free groups as fundamental groups of graphs and modeling their automorphisms as homotopy equivalences of graphs.…

We show, in Zermelo-Fraenkel set theory without the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $\mathbb{R}/\mathbb{Q}$.…

Let $M$ be a smooth manifold and $\mathcal{F}$ a Morse-Bott foliation on $M$ with a compact critical manifold $\Sigma$. Denote by $\mathcal{D}(\mathcal{F})$ the group of diffeomorphisms of $M$ leaving invariant each leaf of $\mathcal{F}$.…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

There is a natural homomorphism of Lie pseudoalgebras from local vector fields to local rotations on a Riemannian manifold. We address the question whether this homomorphism is unique and give a positive answer in the perturbative regime…

Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group…

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

For a homeomorphism $T \colon X \to X$ of a compact metric space $X$, the stabilized automorphism group $\text{Aut}^{(\infty)}(T)$ consists of all self-homeomorphisms of $X$ which commute with some power of $T$. Motivated by the study of…

Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic automorphism. It is shown that while…

Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., the subgroup of the full automorphism group Aut (X) generated by all one-parameter unipotent subgroups. We show…