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Publications Influence

Finite dimensionality of Extn's and Torn's of simple modules over one class of algebras

- V. Bavula
- Mathematics
- 1 July 1991

52 3

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

75 3- PDF

Simple D[X, Y; σ,a]-modules

- V. Bavula
- Mathematics
- 1 December 1992

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.

26 2

The inversion formula for automorphisms of the Weyl algebras and polynomial algebras

- V. Bavula
- Mathematics
- 10 December 2005

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 A… Expand

29 2- PDF

Classification of the simple modules of the quantum Weyl algebra and the quantum plane

- V. Bavula
- Mathematics
- 1997

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

8 2- PDF

The Simple Modules of Certain Generalized Crossed Products

- V. Bavula, F. V. Oystaeyen
- Mathematics
- 15 August 1997

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 a… Expand

40 2- PDF

Indecomposable representations of generalized weyl algebras

- V. Bavula, Viktor I. Bekkert
- Mathematics
- 1 January 2000

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 a… Expand

44 2

The simple modules of the Lie superalgebra osp(1,2)

- V. Bavula, F. V. Oystaeyen
- Mathematics
- 14 June 2000

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 of… Expand

15 2

The algebra of integro-differential operators on an affine line and its modules

- V. Bavula
- Mathematics
- 12 November 2010

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 and… Expand

37 1- PDF

A question of Rentschler and the Dixmier Problem

- V. Bavula
- Mathematics
- 1 November 2001

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 every… Expand

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