Related papers: Automatic Homeomorphicity of Locally Moving Clones

Let M be a connected generic real-analytic CR-submanifold of a finite-dimensional complex vector space E. Suppose that for every point a in M the Lie algebra hol(M,a) of germs of all infinitesimal real-analytic CR-automorphisms of M at a is…

We prove that a large class of metrizable group topologies for subgroups of $\mathbb{R}^n$ and the completions of the subgroups are locally isometric to, respectively, metrizable group topologies for $\mathbb{Z}$ and their completions,…

There are continuum many clones on a three-element set even if they are considered up to \emph{homomorphic equivalence}. The clones we use to prove this fact are clones consisting of \emph{self-dual operations}, i.e., operations that…

A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M'$ is said to be locally rigid if any other holomorphic map $F\colon M \to M'$ which is close enough to $H$ is obtained by composing $H$ with suitable automorphisms…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

We provide a complete classification of when the homeomorphism group of a stable surface, $\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\Sigma)$ to a separable group is necessarily continuous. This result…

Using the notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building, we prove that any (not necessarily discrete) closed, co-compact subgroup of the type-preserving automorphisms group of a locally finite…

Let $R$ be a commutative integral domain with unit, $f$ be a nonconstant monic polynomial in $R[t]$, and $I_f \subset R[t]$ be the ideal generated by $f$. In this paper we study the group of $R$-algebra automorphisms of the $R$-algebra…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $\mathcal{D}(R)$ denote the derived category of $R$-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let $X$ be a…

A loop is automorphic if all its inner mappings are automorphisms. We construct a large family of automorphic loops as follows. Let $R$ be a commutative ring, $V$ an $R$-module, $E=\mathrm{End}_R(V)$ the ring of $R$-endomorphisms of $V$,…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in…

Let A be a locally m-convex Fr\'echet algebra. We give a necessary and sufficient condition for a cyclic Fr\'echet A-module X=A_+/I to be strictly flat, generalizing thereby a criterion of Helemskii and Sheinberg. To this end, we introduce…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

If f is a nontrivial automorphism of a thick building Delta of purely infinite type, we prove that there is no bound on the distance that f moves a chamber. This has the following group-theoretic consequence: If G is a group of…

Let $M$ be a differentiable manifold and $K$ a Lie group. A locally homogeneous triple with structure group $K$ on $M$ is a triple $(g, P\stackrel{p}{\to} M,A)$, where $p:P\to M$ is a principal $K$-bundle on $M$, $g$ is Riemannian metric on…

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for…

Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then $\mathcal{C}$ has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ has a neighborhood $U$ in the complex…

We prove the classical $l = p$ local-global compatibility conjecture for certain regular algebraic cuspidal automorphic representations of weight 0 for GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the…

An automorphism $\alpha$ of a group $G$ is called a commuting automorphism if each element $x$ in $G$ commutes with its image $\alpha(x)$ under $\alpha$. Let $A(G)$ denote the set of all commuting automorphisms of $G$. Rai [Proc. Japan…