Professor Vladimir Bavula
School of Mathematics and Statistics
Professor
+44 114 222 3786
Full contact details
School of Mathematics and Statistics
J15
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
 Research interests

Prof Bavula's research interests are noncommutative Noetherian rings and their modules (especially rings of differential operators and Dmodules), dimensions (the Krull dimension, the global homological dimension, the GelfandKirillov dimension, the filter dimension), graded and filtered algebras, groups of algebra automorphisms, various properties of elements of rings and associated algebraic objects (like derivations and associated algebras, etc).
Prof Bavula is particularly interested in simple infinite dimensional Noetherian noncommutative algebras and in various classification problems associated with them.
 Publications

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Journal articles
 Localizations of a ring at localizable sets, their groups of units and saturations. Mathematics in Computer Science, 16(1).
 Criteria for a direct sum of modules to be a multiplication module over noncommutative rings. Journal of Algebra, 584, 6988.
 The prime spectrum of the universal enveloping algebra of the 1spatial ageing algebra and of U(gl2). Algebra and Discrete Mathematics, 31(1), 116.
 The prime ideals and simple modules of the universal enveloping algebra U(gb ltimes {V_2}). Glasgow Mathematical Journal, 62(S1), S77S98.
 Classification of simple modules of the ore extension K[X][Y;fddX]. Mathematics in Computer Science, 14, 317325. View this article in WRRO
 Skew category algebras. Mathematics in Computer Science, 14, 339346. View this article in WRRO
 The global dimension of the algebras of polynomial integrodifferential operators . Journal of Algebra and Its Applications, 19(02). View this article in WRRO
 The generalized Weyl Poisson algebras and their Poisson simplicity criterion. Letters in Mathematical Physics, 110, 105119. View this article in WRRO
 Generalized Weyl algebras and diskew polynomial rings. Journal of Algebra and Its Applications. View this article in WRRO
 Rings of invariants of finite groups when the bad primes exist. Communications in Algebra, 47(10), 41144124. View this article in WRRO
 Characterization of multiplication commutative rings with finitely many minimal prime ideals. Communications in Algebra. View this article in WRRO
 A remark on the Dixmier Conjecture. Canadian Mathematical Bulletin. View this article in WRRO
 The universal enveloping algebra of the Schrödinger algebra and its prime spectrum. Canadian Mathematical Bulletin, 61(4), 688703. View this article in WRRO
 The prime spectrum of the algebra Kq[X,Y]⋊Uq(sl2) and a classification of simple weight modules. Journal of Noncommutative Geometry, 12(3), 889946. View this article in WRRO
 Criteria for a Ring to have aLeft Noetherian Largest Left Quotient Ring. Algebras and Representation Theory, 21(2), 359373. View this article in WRRO
 Classification of Simple Weight Modules over the Schrödinger Algebra. Canadian Mathematical Bulletin, 61(1), 1639. View this article in WRRO
 Indecomposable generalized weight modules over the algebra of polynomial integrodifferential operators. Proceedings of the American Mathematical Society. View this article in WRRO
 View this article in WRRO The universal enveloping algebra U(sl2 sdir V2), its prime spectrum and a classification of its simple weight modules. JOURNAL OF LIE THEORY, 28(2), 525560.
 On approximations of the de Rham complex and their cohomology. Communications in Algebra, 46(4), 14471463. View this article in WRRO
 Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings. Mathematics in Computer Science, 11(34), 253268. View this article in WRRO
 Criteria for a ring to have a left Noetherian left quotient ring. Journal of Pure and Applied Algebra. View this article in WRRO
 The quantum euclidean algebra and its prime spectrum. Israel Journal of Mathematics, 219(2), 929958. View this article in WRRO
 The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence. Communications in Algebra, 45(3), 11141133. View this article in WRRO
 Torsion simple modules over the quantum spatial ageing algebra. Communications in Algebra, 45(10), 41664189. View this article in WRRO
 Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules. Journal of Mathematical Physics, 58(1). View this article in WRRO
 The groups K1(Sn , p) of the algebra of onesided inverses of a polynomial algebra. Publicationes Mathematicae Debrecen, 90(12), 5590. View this article in WRRO
 Weakly left localizable rings. Communications in Algebra, 118. View this article in WRRO
 The Prime Spectrum and Simple Modules Over the Quantum Spatial Ageing Algebra. Algebras and Representation Theory, 19(5), 11091133. View this article in WRRO
 The classical left regular left quotient ring of a ring and its semisimplicity criteria. Journal of Algebra and Its Applications. View this article in WRRO
 The groups of automorphisms of the Lie algebras of triangular polynomial derivations. Journal of Pure and Applied Algebra, 218(5), 829851. View this article in WRRO
 Алгебры Ли треугольных полиномиальных дифференцирований и критерий изоморфности их факторалгебр Ли. Известия Российской академии наук. Серия математическая, 77(6), 344.
 The algebra of integrodifferential operators on an affine line and its modules. Journal of Pure and Applied Algebra, 217(3), 495529.
 K
1 (S1 ) and the group of automorphisms of the algebra S2 of onesided inverses of a polynomial algebra in two variables. Journal of KTheory, 10(3), 583601.  Every monomorphism of the Lie algebra of triangular polynomial derivations is an automorphism. Comptes Rendus Mathematique, 350(1112), 553556.
 The group of automorphisms of the Jacobian algebra An. Journal of Pure and Applied Algebra.
 The group of automorphisms of the algebra of polynomial integrodifferential operators. Journal of Algebra, 348(1), 233263.
 Generators and Defining Relations for the Ring of Differential Operators on a Smooth Affine Algebraic Variety. Algebras and Representation Theory, 13(2), 159187.
 Generators and defining relations for the ring of differential operators on a smooth affine algebraic variety in prime characteristic. Journal of Algebra, 323(4), 10361051.
 The Jacobian map, the Jacobian group and the group of automorphisms of the Grassmann algebra. Bulletin de la Société Mathématique de France, 138, 39117.
 Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic. Representation Theory  An electronic journal of the AMS, 13, 182227.
 Finite generation of the group of eigenvalues for sets of derivations or automorphisms of division algebras. Communications in Algebra, 36(6), 21952201.
 DIXMIER'S PROBLEM 6 FOR SOMEWHAT COMMUTATIVE ALGEBRAS AND DIXMIER'S PROBLEM 3 FOR THE RING OF DIFFERENTIAL OPERATORS ON A SMOOTH IRREDUCIBLE AFFINE CURVE. Journal of Algebra and Its Applications, 04(05), 577586.
 Luroth field extensions. J PURE APPL ALGEBRA, 199(13), 110.
 Structure of maximal commutative subalgebras of the first Weyl Algebra. Annali dell'Universita di Ferrara, 51(1), 114.
 GelfandKirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras. J REINE ANGEW MATH, 582, 6185.
 Solutions to two questions about the Weyl algebras. P AM MATH SOC, 133(6), 15871591.
 Simple modules of the WittenWoronowicz algebra. J ALGEBRA, 271(2), 827845.
 A question of Rentschler and the Dixmier problem. Annals of Mathematics, 154(3), 683702.
 Krull dimension of generalized Weyl algebras with noncommutative coefficients. Journal of Algebra, 235(1), 315358.
 Generalized Weyl algebras are tensor Krull minimal. Journal of Algebra, 239(1), 93111.
 Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2. T AM MATH SOC, 353(6), 21932214.
 The simple modules of the Lie superalgebra osp(1,2). J PURE APPL ALGEBRA, 150(1), 4152.
 Simple holonomic modules over the second Weyl algebra A(2). ADV MATH, 150(1), 80116.
 The extension group of the simple modules over the first Weyl algebra. Bulletin of the London Mathematical Society, 32(2), 182190.
 Isomorphism problems and groups of automorphisms for generalized Weyl algebras. T AM MATH SOC, 353(2), 769794.
 Indecomposable representations of generalized Weyl algebras. COMMUN ALGEBRA, 28(11), 50675100.
 A Bernsteingabberjoseph theorem for affine algebras. Proceedings of the Edinburgh Mathematical Society, 42(2), 311332.
 The simple modules of the ore extensions with coefficients from a Dedekind ring. COMMUN ALGEBRA, 27(6), 26652699.
 Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients. J ALGEBRA, 208(1), 134.
 Krull, GelfandKirillov, and filter dimensions of simple affine algebras. J ALGEBRA, 206(1), 3339.
 The simple modules of certain generalized crossed products. J ALGEBRA, 194(2), 521566.
 Classification of modules of dimension n and multiplicity one over the weyl algebraA n. Ukrainian Mathematical Journal, 48(5), 643651.
 Классификация модулей размерности Гельфанда  Кириллова $n$ и кратности 1 над алгеброй Вейля $A_n$. Известия Российской академии наук. Серия математическая, 60(5), 312.
 Classification of modules of gel'fandkirillov dimension n and multiplicity 1 over the weyl algebra a
n . Izvestiya Mathematics, 60(5), 877885.  Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras. B SCI MATH, 120(3), 293335.
 Filter dimension of algebras and modules, a simplicity criterion of generalized Weyl algebras. COMMUN ALGEBRA, 24(6), 19711992.
 IDENTIFICATION OF THE HILBERT FUNCTION AND POINCARESERIES, AND THE DIMENSION OF MODULES OVER FILTERED RINGS. RUSS AC SC IZV MATH+, 44(2), 225246.
 EACH SCHURIAN ALGEBRA IS TENSORSIMPLE. COMMUN ALGEBRA, 23(4), 13631367.
 Extreme modules over the Weyl algebra A
n . Ukrainian Mathematical Journal, 45(9), 13271338.  Description of bilateral ideals in a class of noncommutative rings. II. Ukrainian Mathematical Journal, 45(3), 329334.
 Description of bilateral ideals in a class of noncommutative rings. I. Ukrainian Mathematical Journal, 45(2), 223234.
 Computation of H^{*}(sl(2), M) with coefficients in a simple sl(2)module. Functional Analysis and Its Applications, 26(1), 4546.
 Simple D[X, Y; σ, a]modules. Ukrainian Mathematical Journal, 44(12), 15001511.
 Finite dimensionality of Ext^{n}'s and Tor
n 's of simple modules over one class of algebras. Functional Analysis and Its Applications, 25(3), 229230.  Classification of simple sℓ(2)Modules and finitedimensionality of the module of extensions of simple sℓ(2)modules. Ukrainian Mathematical Journal, 42(9), 10441049.
 Some generalizations of the Eisenstein criterion. Ukrainian Mathematical Journal, 42(7), 873875.
 EXCITATION OF NUCLEARLEVELS OF ANOMALOUS ROTATIONAL BAND AT THE DIFFRACTIONAL SCATTERING OF NEUTRONS. IZV VUZ FIZ+, 32(8), 107108.
 View this article in WRRO Left localizable rings and their characterizations.
 The group of automorphisms of the Lie algebra of derivations of a field of rational functions.
 View this article in WRRO Left localizations of left Artinian rings.
 View this article in WRRO The group of automorphisms of the Lie algebra of derivations of a polynomial algebra.
 View this article in WRRO The largest strong left quotient ring of a ring.
 View this article in WRRO The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence.
 View this article in WRRO The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras.
 View this article in WRRO New criteria for a ring to have a semisimple left quotient ring.
 Characterizations of left orders in left Artinian rings.
 Every monomorphism of the Lie algebra of unitriangular polynomial derivations is an automorphism.
 Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras.
 The algebra of polynomial integrodifferential operators is a holonomic bimodule over the subalgebra of polynomial differential operators.
 The largest left quotient ring of a ring.
 On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra. View this article in WRRO
 The algebra of integrodifferential operators on an affine line and its modules.
 An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integrodifferential operators.
 An analogue of Hilbert's Syzygy Theorem for the algebra of onesided inverses of a polynomial algebra.
 The group of automorphisms of the algebra of polynomial integrodifferential operators.
 The algebra of integrodifferential operators on a polynomial algebra.
 The group of automorphisms of the algebra of onesided inverses of a polynomial algebra, II.
 The algebra of onesided inverses of a polynomial algebra.
 The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic.
 Extensions of the Frobenius to ring of differential operators on polynomial algebra in prime characteristic.
 Generalizations of two theorems of Ritt on decompositions of polynomial maps.
 View this article in WRRO The group of automorphisms of the first Weyl algebra in prime characteristic and the restriction map.
 View this article in WRRO The Jacobian algebras.
 Derivations and skew derivations of the Grassmann algebras.
 Primary Decompositions for Left Noetherian Rings.
 Factorization of monomorphisms of a polynomial algebra in one variable.
 Morita invariance of the filter dimension and of the inequality of Bernstein.
 Quadratic and cubic invariants of unipotent affine automorphisms.
 The inversion formulae for automorphisms of polynomial algebras and differential operators in prime characteristic.
 Generators and defining relations for ring of invariants of commuting locally nilpotent derivations or automorphisms.
 Simple derivations of differentiably simple Noetherian commutative rings in prime characteristic.
 The inversion formula for automorphisms of the Weyl algebras and polynomial algebras.
 Filter Dimension.
 The Carlitz Algebras.
 Dixmier's Problem 5 for the Weyl Algebra.
 Dixmier's Problem 6 for the Weyl Algebra (the Generic type Problem).
 Classification of the simple modules of the quantum Weyl algebra and the quantum plane. Banach Center Publications, 40(1), 193201.
 View this article in WRRO Simplicity criteria for rings of differential operators.
 View this article in WRRO Explicit description of generalized weight modules of the algebra of polynomial integrodifferential operators $I_n$.
 The PBW Theorem and simplicity criteria for the Poisson enveloping algebra and the algebra of Poisson differential operators.
 The Poisson enveloping algebra and the algebra of Poisson differential operators of a generalized Weyl Poisson algebra.
 Isomorphism problems and groups of automorphisms for Ore extensions $K[x][y; δ]$ (zero characteristic).
 Isomorphism problems and groups of automorphisms for Ore extensions $K[x][y; ffrac{d}{dx} ]$ (prime characteristic).
 Holonomic modules and 1generation in the Jacobian Conjecture.
 Description of biquadratic algebras on 3 generators with PBW basis.
 Localizable sets and the localization of a ring at a localizable set.
Chapters
 The global dimension of the generalized Weyl algebras (pp. 3360). American Mathematical Society
 The prime ideals and simple weight modules of the algebra (pp. 4970). American Mathematical Society
Conference proceedings papers
 The global dimension of the generalized weyl algebras s^{−1}k[h, c][x, y; σ, a]. Contemporary Mathematics, Vol. 751 (pp 3360)
 Orders in Artinian rings, Goldie’s Theorem and the largest left quotient ring of a ring (pp 124) View this article in WRRO
 Krull, GelfandKirillov, Filter, Faithful and Schur dimensions. INFINITE LENGTH MODULES (pp 149166)
 View this article in WRRO The ${rm Jacobian Conjecture}_{2n}$ implies the ${rm Dixmier Problem}_n$
Working papers
 View this article in WRRO The group of automorphisms of the Jacobian algebra $mA_n$.
 ${rm K}_1(mS_1)$ and the group of automorphisms of the algebra $mS_2$ of onesided inverses of a polynomial algebra in two variables.
 View this article in WRRO Finite generation of division subalgebras and of the group of eigenvalues for commuting derivations or automorphisms of division algebras.
 Research group
 Grants

Past grants, as Principal Investigator
The Conjecture Dixmier EPSRC Automorphisms, Derivations and Polynomial IntegroDifferential Operators RS
 Teaching activities

MAS333 Fields MAS438 Fields