相关论文: Differential Isomorphism and Equivalence of Algebr…

We consider differential rings of the form (K[x; y];D), where K is an algebraically closed field of characteristic zero and D : K[x; y] \to K[x; y] is a K-derivation. We study the Automorphism Group of such a ring and give criteria for…

If the bimodule of 1-forms of a differential calculus over an associative algebra is the direct sum of 1-dimensional bimodules, a relation with automorphisms of the algebra shows up. This happens for some familiar quantum space calculi.

Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra $\mv = \{f\big|_V : f \in \cM_d\}$, where $d$ is some integer or $\infty$, $\cM_d$ is the multiplier algebra of the Drury-Arveson space…

In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…

Weyl groups are ubiquitous, and efficient algorithms for them -- especially for the exceptional algebras -- are clearly desirable. In this paper we provide several of these, addressing practical concerns arising naturally for instance in…

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.

We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…

A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…

We present a common framework to study varieties in great generality from a categorical point of view. The main application of this study is in the setting of algebraic categories, where we introduce Birkhoff varieties which are essentially…

Let $A_1$ be the (first) Weyl algebra, and let $G$ be its automorphism group. We study the natural action of $G$ on the space of isomorphism classes of right ideals of $A_1$ (equivalently, of finitely generated rank 1 torsion-free right…

For every variety of algebras over a field, there is a natural definition of a corresponding variety of dialgebras (Loday-type algebras). In particular, Lie dialgebras are equivalent to Leibniz algebras. We use an approach based on the…

We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…

Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular,…

We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…

We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by…

A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

We introduce a class of algebras over a field $\mathbb{F}$ related to directed graphs in which all edges are labeled by nonzero elements of the field $\mathbb{F}$. If all labels are different from $1$, these algebras are axial algebras. We…

This article considers cuspidal curves whose coordinate rings are numerical semigroup algebras. Using a general result about descent of Hopf algebroid structures, their rings of differential operators are shown to be cocommutative and…