Related papers: Dixmier's Problem 5 for the Weyl Algebra

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.

We introduce a new version $kk^{\rm alg}$ of bivariant $K$-theory that is defined on the category of all locally convex algebras. A motivating example is the Weyl algebra $W$, i.e. the algebra generated by two elements satisfying the…

We give an algebraic classification of complex $5$-dimensional one-generated nilpotent terminal algebras.

The aim of this paper is to give two new algorithms, which are elimination free, to find polynomial and rational solutions for a given holonomic system associated to a set of linear differential operators in the Weyl algebra D = k<x_1, ...,…

We study the Weyl-type solutions of the differential system with a singularity $y'-x^{-1}Ay-q(x)y=\rho By$ in the case of integrable potential $q(\cdot)$.

We augment the method of Wooley (2015) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real polynomials with partially prescribed coefficients. We also…

In this paper, we will define the Brauer algebras of Weyl types, and describe some propositions of these algebras. Especially, we prove the result of type $G_2$ to accomplish our project of Brauer algebras of non-simply laced types.

Let $D$ be a divisor in ${\bf C}^n$. We present methods to compare the ${\mathcal D}$-module of the meromorphic functions ${\mathcal O}[* D]$ to some natural approximations. We show how the analytic case can be treated with computations in…

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as…

We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.

We provide an overview of the connections between Bell's inequalities and algebraic structure.

The aim of this paper is to prove a version of Lie's theorem for the supertropical algebra.

We present some questions and suggestion on the second part of the Hilbert 16th problem

In this note, we mainly consider the extended Weyl algebra of two generators (u,v), that is, the algebra generated by u,v with the fundamental commutation relation. Weyl algebra is realized on the space of polynomials of u and v by defining…

An technically interesting proof of a known theorem.

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.

We propose a method for computing upper bounds for the Heilbronn problem for triangles.

An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.