Related papers: Two properties of endomorphisms of Weyl algebras

Endomorphisms of Weyl algebras are studied using bimodules. Initially, for a Weyl algebra over a field of characteristic zero, Bernstein's inequality implies that holonomic bimodules finitely generated from the right or left form a monoidal…

We prove that every endomorphism of a simple quantum generalized Weyl algebra $A$ over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms…

We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several…

We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…

The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any…

We present an independent short proof of the main result of arXiv:0706.3725 that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with…

Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts. We describe the structure of endomorphisms and their asymptotic lifts in some…

In one of our recent papers, the associative and the Lie algebras of Weyl type $A[D]=A\otimes F[D]$ were defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of any characteristic,…

We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras O_n, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their…

We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to an Abelian variety over a field of characteristic zero as a morphism vanishes if and only if it…

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of…

We proved that, in characteristic 0, if two dominant endomorphisms of the projective plane of degree at least 2 are conjugate by some birational transformation, then they are conjugate by an automorphism. We also gave counterexamples in…

In this paper we address the problem of classification of simple weight modules over weak generalized Weyl algebras of rank one. The principal difference between weak generalized Weyl algebras and generalized weight algebras is that weak…

Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove that the Dixmier conjecture for the first Weyl algebra is true, i.e. each algebra endomorphism of the algebra $A_1$ is an…

We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by…

We determine the blocks of the walled Brauer algebra in characteristic zero. These can be described in terms of orbits of the action of a Weyl group of type $A$ on a certain set of weights. In positive characteristic we give a linkage…

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…

In this paper we study a correspondence between cyclic modules over the first Weyl algebra and planar algebraic curves in positive characteristic. In particular, we show that any such curve has a preimage under a morphism of certain…

We introduce the first hom-associative Weyl algebras over a field of prime characteristic as a generalization of the first associative Weyl algebra in prime characteristic. First, we study properties of hom-associative algebras constructed…

We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as hom-associative algebras. We also show that these…