相关论文: On the isotropy of differential Ore extensions

In this paper, we study the isotropy group of Lotka-Volterra derivations of $K[x_{1},\cdots,x_{n}]$, i.e., a derivation $d$ of the form $d(x_{i})=x_{i}(x_{i-1}-C_{i}x_{i+1})$. If $n=3$ or $n \geq 5$, we have shown that the isotropy group of…

We study sigma-derivations of the quantum plane and their isotropy groups under the conjugation action of automorphisms. For the case where q is different from plus or minus one, we classify all sigma-derivations for an arbitrary…

In the present work we consider differential rings of the form $(\mathcal B,D)$ where $\mathcal B$ is a Danielewski surface and $D$ is a locally nilpotent derivation on $\mathcal B$. Influenced by several recent works, we describe the…

In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator…

Let $\L (f) = K[x][y; f\frac{d}{dx} ]$ be an Ore extension of a polynomial algebra $K[x]$ over a field $K$ of characteristic zero where $f\in K[x]$. For a given polynomial $f$, the automorphism group of the algebra $\L (f) $ is explicitly…

Let $k$ be a field of characteristic zero, and let $i$ and $n$ be positive integers with $i\geq 2$ and $n>i$. Consider a non-invertible $k$-derivation $d_i$ of the polynomial ring $k[x_1,\ldots,x_i]$. Let $d_n$ be an extension of $d_i$ to a…

Given an algebraically closed field $k$ of characteristic zero, we consider in this paper $k$-algebras of the form $$A_{c,q}=k[x,y,z]/\big(c(x)z-q(x,y)\big),$$ where $c(x)\in k[x]$ is a polynomial of degree at least two and $q(x,y)\in…

This paper investigates the isotropy groups of derivations on the Quantum Plane $\Bbbk_q[x, y]$, defined by the relation $yx = qxy$, where $q \in \Bbbk^*$, with $q^2\neq 1$. The main goal is to determine the automorphisms of the Quantum…

Let $\Dh$ and $A$ be unital and separable $C^{*}$-algebras; let $\Dh$ be strongly self-absorbing. It is known that any two unital $^*$-homomorphisms from $\Dh$ to $A \otimes \Dh$ are approximately unitarily equivalent. We show that, if…

Let K be an algebraically closed field of characteristic zero. We study the tame isotropy group Tame_D(K[X,Y]) of locally finite derivations of the polynomial ring K[X,Y], using Van den Essen's classification up to conjugation. For each…

Let $G$ be a finite group of odd order admitting an involutory automorphism $\phi$. We obtain two results bounding the exponent of $[G,\phi]$. Denote by $G_{-\phi}$ the set $\{[g,\phi]\,\vert\, g\in G\}$ and by $G_{\phi}$ the centralizer of…

This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\Def ^{\h}(E)$,…

Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite…

Let 1-> H -> G _> Q -> 1 be an exact sequence of groups. In the paper of R. Oliver and J. Ventura, TAMS,362(2009), the following exact sequence was developed for centric extensions, i.e the centralizer of H in G is contained in H, 0->…

If $A$ is an algebra with finite right global dimension, then for any automorphism $\alpha$ and $\alpha$-derivation $\delta$ the right global dimension of $A[t; \alpha, \delta]$ satisfies \[ \text{rgld} \, A \le \text{rgld} \, A[t; \alpha,…

We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…

We study zero entropy automorphisms of a compact K\"ahler manifold $X$. Our goal is to bring to light some new structures of the action on the cohomology of $X$, in terms of the so-called dynamical filtrations on $H^{1,1}(X, {\mathbb R})$.…

Let $G$ be a finitely generated group with an automorphism $\varphi\in{\rm Aut}(G)$, or an outer automorphism $\phi\in{\rm Out}(G)$. Suppose that $G$ decomposes into simpler pieces on which the growth behaviour of $\varphi$ and $\phi$ is…

Sufficient and necessary conditions for an extension of a skew-derivation $(\delta_R,\alpha_R)$ of an associative $\mathbb{F}$-algebra $R$ to a skew derivation $(\delta_S,\alpha_S)$ on an extension $S$ of $R$ by $\mathbb{F}$ or a {\em…

In this paper, we study the isotropy groups of locally finite derivations of the polynomial ring $\mathbb{K}[X,Y]$, using Van den Essen's classification of locally finite derivations in two variables. We compare the isotropy group of a…