Related papers: 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…