Related papers: Locally nilpotent derivations on $\mathbb{A}^2$-fi…

Let $\mathcal{A}$ be a Hom-finite additive Krull-Schmidt $k$-category where $k$ is an algebraically closed field. Let ${\rm mod} \mathcal{A}$ denote the category of locally finite dimensional $\mathcal{A}$-modules, that is, the category of…

Let k be an algebraically closed field of characteristic zero, D a locally nilpotent derivation on the polynomial ring k[X_1, X_2,X_3,X_4] and A the kernel of D. A question of M. Miyanishi asks whether projective modules over A are…

In this paper we prove some results on the sufficiency of codimension-one fibre conditions for a flat algebra with a retraction to be locally $\mathbb{A}^1$ or at least an $\mathbb{A}^1$-fibration.

We study Dirichlet forms defined by nonintegrable L\'evy kernels whose singularity at the origin can be weaker than that of any fractional Laplacian. We show some properties of the associated Sobolev type spaces in a bounded domain, such as…

In this paper we prove a perturbative result for a class of $\mathbb Z^2$ actions on Heisenberg nilmanifolds, which have Diophantine properties. Along the way we prove cohomological rigidity and obtain a tame splitting for the cohomology…

Let $(A,\m)$ be a Noetherian local ring with infinite residue field and let $I$ be an ideal in $A$ and let $F(I) = \oplus_{n \geq 0}I^n/\m I^n$ be the fiber-cone of $I$. We prove certain relations among the Hilbert coefficients of $F(I)$…

A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for…

We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…

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…

The aim of this paper is to propose a theory of derivations for quandles. Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$ to $A$ are introduced as twisted analogues of quandle homomorphisms. It is shown that…

The paper studies the dimensions of irreducible components of commuting varieties of (restricted) nilpotent $r$-tuples in a classical Lie algebra $\mathfrak{g}$ defined over an algebraically closed field $k$. As applications, we obtain some…

The main result of the paper is the following theorem. Let $q$ be a prime and $A$ an elementary abelian group of order $q^3$. Suppose that $A$ acts coprimely on a profinite group $G$ and assume that $C_G(a)$ is locally nilpotent for each…

In this short paper, we establish the local Noetherian property for the linear categories of Brauer, partition algebras, and other related categories of diagram algebras with no restrictions on their various parameters.

Let \(\mathcal{A}\) be a unital Banach algebra such that any Jordan derivation from \(\mathcal{A}\) into any \(\mathcal{A}\)-bimodule \(\mathcal{M}\) is a derivation. We prove that any 2-local derivation from the algebra $M_n(\mathcal{A})$…

We prove that a Lie conformal algebra L with bounded locality function is embeddable into an associative conformal algebra A with the same bound on the locality function. If L is nilpotent, then so is A, and the nilpotency index remains the…

We analyse the $L^2$ Hilbert complexes naturally associated to a non-compact complex manifold, namely the ones which originate from the Dolbeault and the Aeppli-Bott-Chern complexes. In particular we define the $L^2$ Aeppli-Bott-Chern…

We describe the set of all locally nilpotent derivations of the quotient ring $\mathbb{K}[X,Y,Z]/(f(X)Y - \varphi(X,Z))$ constructed from the defining equation $f(X)Y = \varphi(X,Z)$ of a generalized Danielewski surface in $\mathbb K^3$ for…

We prove that each local Lie $n$-derivation is a Lie $n$-derivation under mild assumptions on the unital algebras with a nontrivial idempotent. As applications, we obtain descriptions of local Lie $n$-derivations on generalized matrix…

We set up the geometric background necessary to extend rigid cohomology from the case of algebraic varieties to the case of general locally noetherian formal schemes. In particular, we generalize Berthelot's strong fibration theorem to adic…

We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier…