Fix $ f\in {\mathbf {C}}[X] $. Define $ R={\mathbf {C}}[A, B, H] $ subject to the relations\[HA-
AH= A,\quad HB-BH=-B,\quad AB-BA= f (H)\]. We study these algebras (for different $ f $) …

The type-A Kleinian singularities are the surfaces of the form C 2/G where G is a finite cyclic
subgroup of SL 2 (C). The standard noncommutative analog is the fixed ring of the Weyl …

arXiv:2305.01609v1 [math.RA] 2 May 2023 Page 1 arXiv:2305.01609v1 [math.RA] 2 May 2023
THE WEYL ALGEBRA AND ITS FRIENDS: A SURVEY JASON GADDIS Abstract. We survey …

Résumé Soit G un sous-groupe fini de Sp (2n, C) opérant par automorphismes dans
l'algèbre de Weyl A n (C). Nous calculons les groupes d'homologie et de cohomologie de …

Let R be an iterated Ore extension k [y][z; o, 6] of the complex number field k, with oa k-
automorphism of k [y] and 6 a u-derivation of k [y] vanishing on k. We suppose that the center …

We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold (ℝ m, α)
we consider the Poisson orbivariety (. The Kontsevich star product on functions on (ℝ m) n …

Graded twisting of comodule algebras and module categories Page 1 J. Noncommut. Geom.
12 (2018), 331–368 DOI 10.4171/JNCG/278 Journal of Noncommutative Geometry © …

Rings of invariants can have nice homological properties even if they do not have finite
global dimension. Watanabe's Theorem [W] gives conditions when the fixed subring of a …

Let PG be the quotient variety of the affine plane by the action of a finite group G⊂ SL (2, ℂ);
then PG inherits in a natural way a Poisson algebra structure. Let A 1 (ℂ) be the first Weyl …

In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite
group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the …