相关论文: Dixmier's Problem 5 for the Weyl Algebra

We introduce Weyl n-algebras and show how their factorization homology may be used to define invariants of manifolds. In the appendix we heuristically explain why these invariants must be perturbative Chern-Simons invariants.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We give a q-analogue of Gauss' divisibility theorem

Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena

Weyl denominator identity for finite-dimensional Lie superalgebras, conjectured by V.~Kac and M.~Wakimoto in 1994, is proven.

A peeling theorem for the Weyl tensor in higher dimensional Lorentzian manifolds is presented. We obtain it by generalizing a proof from the four dimensional case. We derive a generic behavior, discuss interesting subcases and retrieve the…

We sketch several proofs of F\'ary--Milnor theorem.

In this note we solve the isomorphism problem for the multiparameter quantized Weyl algebras, in the case when none of the deformation parameters q_i is a root of unity, over an arbitrary field.

A new class of Poisson algebras, the class of {\em generalized Weyl Poisson algebras}, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl…

The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.

We classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl-Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor…

We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.

In a recent Comment on the paper "Dark matter as a Weyl geometric effect", by Burikham et al., Phys. Rev. D 107, 064008 (2023), posted on arxiv. org as eprint arXiv:2306.11926, it was claimed that the exact solution found in the above…

In this paper, we derive $C^2$ estimates for a class of mixed Hessian type equations with Dirichlet boundary condition, and obtain the existence theorem of admissible solutions for the classical Dirichlet problem of these mixed Hessian type…

A Gr\"obner basis computation for the Weyl algebra with respect to a tropical term order and by using a homogenization-dehomogenization technique is sufficiently sluggish. A significant number of reductions to zero occur. To improve the…

The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in…

We define analogues of the Casimir and Dirac operators for graded affine Hecke algebras, and establish a version of Parthasarathy's Dirac operator inequality. We then prove a version of Vogan's Conjecture for Dirac cohomology. The…

In view of a well-known theorem of Dixmier, its is natural to consider primitive quotients of $U_q^+(\mathfrak{g})$ as quantum analogues of Weyl algebras. In this work, we study these primitive quotients in the $G_2$ case and compute their…