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 …

Let Γ be a finite subgroup of SL2 (k), for k an algebraically closed field of characteristic zero.
W. Crawley-Boevey and the author [8] have introduced some noncommutative quantizations …

The aim of these notes is to collect and motivate the basic localization toolbox for the
geometric study of" spaces" locally described by noncommutative rings and their categories …

It is proved that Zhu's algebra for the vertex operator algebra associated to a positive-definite
even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of a certain …

Theory of the quantized flag manifold as a quasi-scheme (non-commutative scheme) has
been developed by Lunts-Rosenberg [15]. They have formulated an analogue of the …

In this paper we study rings of differential operators for modules of covariants for one-
dimensional tori. In particular we analyze when they are Morita equivalent, when they are …

Motivated by the study of invariant rings of finite groups on the first Weyl algebras A 1 and
finding interesting families of new noetherian rings, a class of algebras similar to U (sl 2) was …

The theory of enveloping algebras of Lie algebras underwent an explosive development
during the period 1975-1985. This was due in part to the very rich structure afforded by the …

The recent proof of the Kazhdan-Lusztig conjectures involved a number of deep results from
some diverse areas of mathematics: intersection cohomology, D-modules, holonomic …