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Isomorphism problems and groups of automorphisms for generalized Weyl algebras
We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to U(sl2) introduced by S. P.Expand
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Simple D[X, Y; σ,a]-modules
The article classifies simple modules over a generalized Weyl algebra of degree I with basis ring D that is a commutative domain with limited minimality condition.
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The inversion formula for automorphisms of the Weyl algebras and polynomial algebras
Let An be the nth Weyl algebra and Pm be a polynomial algebra in m variables over a field K of characteristic zero. The following characterization of the algebras {An⊗Pm} is proved: an algebra AExpand
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Classification of the simple modules of the quantum Weyl algebra and the quantum plane
for all α, β ∈ D and i, j ∈ Z and some map (a “2-cocycle”) c : Z×Z→ Z(D), the centre of D. Throughout the paper a “module” means a left module. Nontrivial examples of R are generalized Weyl algebras.Expand
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The Simple Modules of Certain Generalized Crossed Products
Abstract We consider a Dedekind domainDand aZ-graded ring R = ;⊕ i ∈ Z R i withR0 = Dand eachRi = Dvibeing a freeD-module of rank 1. The structure ofRis described by an automorphism ofDand aExpand
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Indecomposable representations of generalized weyl algebras
For a class of generalized Weyl algebras which includes the Weyl algebras An a criterion is given as to when the category of indecomposable weight and generalized weight modules with supports from aExpand
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The simple modules of the Lie superalgebra osp(1,2)
Abstract A classification (up to irreducible elements of a certain Euclidean ring) of the simple modules of the Lie superalgebra osp (1,2) (over an uncountable algebraically closed field ofExpand
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The algebra of integro-differential operators on an affine line and its modules
For the algebra $\mI_1= K $ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left andExpand
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A question of Rentschler and the Dixmier Problem
The following theorem is the main result of the paper. THEOREM. Let R and T be somewhat commutative algebras with the same holonomic number and let φ: R → T be an algebra homomorphism. Then everyExpand
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