Professor Vladimir Bavula
School of Mathematical and Physical Sciences
Professor
v.bavula@sheffield.ac.uk
+44 114 222 3786
+44 114 222 3786
J15, Hicks Building
Full contact details
Professor Vladimir Bavula
School of Mathematical and Physical Sciences
J15
Hicks Building
Hounsfield Road
91直播
S3 7RH
School of Mathematical and Physical Sciences
J15
Hicks Building
Hounsfield Road
91直播
S3 7RH
- Research interests
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Prof Bavula's research interests are noncommutative Noetherian rings and their modules (especially rings of differential operators and D-modules), dimensions (the Krull dimension, the global homological dimension, the Gelfand-Kirillov 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 non-commutative algebras and in various classification problems associated with them.
- Publications
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All publications
Journal articles
- . Journal of Pure and Applied Algebra, 229(1), 107776-107776.
- . Comptes Rendus. Math茅matique, 362(G7), 731-738.
- . Journal of Noncommutative Geometry.
- . Journal of Algebra, 631, 695-730.
- . Journal of Algebra and Its Applications, 2550035.
- . Journal of Algebra and Its Applications, 2450218.
- Vitaliy M. Bondarenko To the 75th anniversary. ALGEBRA AND DISCRETE MATHEMATICS, 36(1), C-J.
- . Journal of Algebra, 610, 38-75.
- . Mathematics in Computer Science, 16(1).
- . Tokyo Journal of Mathematics, -1(-1).
- . Journal of Algebra, 584, 69-88.
- . Algebra and Discrete Mathematics, 31(1), 1-16.
- . Asian Journal of Mathematics, 25(5), 727-756.
- . Glasgow Mathematical Journal, 62(S1), S77-S98.
- . Communications in Algebra, 48(10), 4554-4554.
- . Mathematics in Computer Science, 14, 317-325.
- . Mathematics in Computer Science, 14, 339-346.
- . Journal of Algebra and Its Applications, 19(02).
- . Letters in Mathematical Physics, 110, 105-119.
- . Journal of Algebra and Its Applications.
- . Communications in Algebra, 47(10), 4114-4124.
- . Communications in Algebra.
- . Canadian Mathematical Bulletin.
- Yuriy Drozd (dedicated to 75th Birthday). ALGEBRA & DISCRETE MATHEMATICS, 28(2), C-F.
- VOLODYMYR KYRYCHENKO (dedicated to the 75th anniversary). ALGEBRA & DISCRETE MATHEMATICS, 27(1).
- . Canadian Mathematical Bulletin, 61(4), 688-703.
- . Journal of Noncommutative Geometry, 12(3), 889-946.
- . Algebras and Representation Theory, 21(2), 359-373.
- . Canadian Mathematical Bulletin, 61(1), 16-39.
- . Proceedings of the American Mathematical Society.
- 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), 525-560.
- . Communications in Algebra, 46(4), 1447-1463.
- . Mathematics in Computer Science, 11(3-4), 253-268.
- . Journal of Pure and Applied Algebra.
- . Israel Journal of Mathematics, 219(2), 929-958.
- . Communications in Algebra, 45(3), 1114-1133.
- . Communications in Algebra, 45(10), 4166-4189.
- . Journal of Mathematical Physics, 58(1).
- . Publicationes Mathematicae Debrecen, 90(1-2), 55-90.
- Sergiy Ovsienko (01.05.1953-25.01.2016). ALGEBRA & DISCRETE MATHEMATICS, 23(1), C-F.
- . Communications in Algebra, 1-18.
- . Algebras and Representation Theory, 19(5), 1109-1133.
- . Journal of Algebra and Its Applications.
- . Journal of Pure and Applied Algebra, 218(5), 829-851.
- . 袠蟹胁械褋褌懈褟 袪芯褋褋懈泄褋泻芯泄 邪泻邪写械屑懈懈 薪邪褍泻. 小械褉懈褟 屑邪褌械屑邪褌懈褔械褋泻邪褟, 77(6), 3-44.
- . Journal of Pure and Applied Algebra, 217(3), 495-529.
- . Journal of K-Theory, 10(3), 583-601.
- . Comptes Rendus Mathematique, 350(11-12), 553-556.
- The group of automorphisms of the Jacobian algebra An. Journal of Pure and Applied Algebra.
- . Journal of Algebra, 348(1), 233-263.
- . Algebras and Representation Theory, 13(2), 159-187.
- . Journal of Algebra, 323(4), 1036-1051.
- The Jacobian map, the Jacobian group and the group of automorphisms of the Grassmann algebra. Bulletin de la Soci茅t茅 Math茅matique de France, 138, 39-117.
- . Representation Theory - An electronic journal of the AMS, 13, 182-227.
- . Communications in Algebra, 36(6), 2195-2201.
- . Journal of Algebra and Its Applications, 04(05), 577-586.
- . J PURE APPL ALGEBRA, 199(1-3), 1-10.
- . Annali dell'Universita di Ferrara, 51(1), 1-14.
- Gelfand-Kirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras. J REINE ANGEW MATH, 582, 61-85.
- Solutions to two questions about the Weyl algebras. P AM MATH SOC, 133(6), 1587-1591.
- . J ALGEBRA, 271(2), 827-845.
- . Annals of Mathematics, 154(3), 683-702.
- . Journal of Algebra, 235(1), 315-358.
- . Journal of Algebra, 239(1), 93-111.
- Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2. T AM MATH SOC, 353(6), 2193-2214.
- The simple modules of the Lie superalgebra osp(1,2). J PURE APPL ALGEBRA, 150(1), 41-52.
- Simple holonomic modules over the second Weyl algebra A(2). ADV MATH, 150(1), 80-116.
- . Bulletin of the London Mathematical Society, 32(2), 182-190.
- Isomorphism problems and groups of automorphisms for generalized Weyl algebras. T AM MATH SOC, 353(2), 769-794.
- Indecomposable representations of generalized Weyl algebras. COMMUN ALGEBRA, 28(11), 5067-5100.
- . Proceedings of the Edinburgh Mathematical Society, 42(2), 311-332.
- The simple modules of the ore extensions with coefficients from a Dedekind ring. COMMUN ALGEBRA, 27(6), 2665-2699.
- Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients. J ALGEBRA, 208(1), 1-34.
- Krull, Gelfand-Kirillov, and filter dimensions of simple affine algebras. J ALGEBRA, 206(1), 33-39.
- The simple modules of certain generalized crossed products. J ALGEBRA, 194(2), 521-566.
- . Ukrainian Mathematical Journal, 48(5), 643-651.
- . 袠蟹胁械褋褌懈褟 袪芯褋褋懈泄褋泻芯泄 邪泻邪写械屑懈懈 薪邪褍泻. 小械褉懈褟 屑邪褌械屑邪褌懈褔械褋泻邪褟, 60(5), 3-12.
- . Izvestiya Mathematics, 60(5), 877-885.
- Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras. B SCI MATH, 120(3), 293-335.
- Filter dimension of algebras and modules, a simplicity criterion of generalized Weyl algebras. COMMUN ALGEBRA, 24(6), 1971-1992.
- IDENTIFICATION OF THE HILBERT FUNCTION AND POINCARE-SERIES, AND THE DIMENSION OF MODULES OVER FILTERED RINGS. RUSS AC SC IZV MATH+, 44(2), 225-246.
- EACH SCHURIAN ALGEBRA IS TENSOR-SIMPLE. COMMUN ALGEBRA, 23(4), 1363-1367.
- . Ukrainian Mathematical Journal, 45(9), 1327-1338.
- . Ukrainian Mathematical Journal, 45(3), 329-334.
- . Ukrainian Mathematical Journal, 45(2), 223-234.
- . Functional Analysis and Its Applications, 26(1), 45-46.
- . Ukrainian Mathematical Journal, 44(12), 1500-1511.
- . Functional Analysis and Its Applications, 25(3), 229-230.
- . Ukrainian Mathematical Journal, 42(9), 1044-1049.
- . Ukrainian Mathematical Journal, 42(7), 873-875.
- EXCITATION OF NUCLEAR-LEVELS OF ANOMALOUS ROTATIONAL BAND AT THE DIFFRACTIONAL SCATTERING OF NEUTRONS. IZV VUZ FIZ+, 32(8), 107-108.
- . Glasgow Mathematical Journal, 1-5.
- . Proceedings of the American Mathematical Society.
- Left localizable rings and their characterizations.
- The group of automorphisms of the Lie algebra of derivations of a field
of rational functions.
- Left localizations of left Artinian rings.
- The group of automorphisms of the Lie algebra of derivations of a
polynomial algebra.
- The largest strong left quotient ring of a ring.
- The groups of automorphisms of the Lie algebras of polynomial vector
fields with zero or constant divergence.
- The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras.
- 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.
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- The algebra of polynomial integro-differential operators is a holonomic
bimodule over the subalgebra of polynomial differential operators.
- The largest left quotient ring of a ring.
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- The algebra of integro-differential operators on an affine line and its
modules.
- An analogue of the Conjecture of Dixmier is true for the algebra of
polynomial integro-differential operators.
- An analogue of Hilbert's Syzygy Theorem for the algebra of one-sided
inverses of a polynomial algebra.
- The group of automorphisms of the algebra of polynomial
integro-differential operators.
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- The group of automorphisms of the algebra of one-sided inverses of a
polynomial algebra, II.
- The algebra of one-sided 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.
- The group of automorphisms of the first Weyl algebra in prime
characteristic and the restriction map.
- 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).
- . Banach Center Publications, 40(1), 193-201.
- Simplicity criteria for rings of differential operators.
- Explicit description of generalized weight modules of the algebra of
polynomial integro-differential 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
$K[x][y; 未]$ (zero characteristic).
- Isomorphism problems and groups of automorphisms for Ore extensions
$K[x][y; ffrac{d}{dx} ]$ (prime characteristic).
- Holonomic modules and 1-generation in the Jacobian Conjecture.
- Description of bi-quadratic algebras on 3 generators with PBW basis.
- Localizable sets and the localization of a ring at a localizable set.
Chapters
- (pp. 33-60). American Mathematical
Society
- (pp. 49-70). American Mathematical
Society
- , HANDBOOK OF ALGEBRA, VOL 4 (pp. 77-105).
Conference proceedings papers
- . CATEGORICAL, HOMOLOGICAL AND COMBINATORIAL METHODS IN ALGEBRA, Vol. 751 (pp 33-60)
- (pp 1-24)
- Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions. INFINITE LENGTH MODULES (pp 149-166)
- The ${rm Jacobian Conjecture}_{2n}$ implies the ${rm Dixmier
Problem}_n$
Working papers
- 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 one-sided inverses of a polynomial algebra in two variables.
- Finite generation of division subalgebras and of the group of
eigenvalues for commuting derivations or automorphisms of division algebras.
Preprints
- Affirmative answer to the Question of Leroy and Matczuk on injectivity
of endomorphisms of semiprime left Noetherian rings with large images.
- , arXiv.
- , arXiv.
- , arXiv.
- General theory of localizations of rings and modules, arXiv.
- Embeddings of semiprime rings into semisimple Artinian rings, arXiv.
- Classification of multiplication modules over multiplication rings with finitely many minimal primes, arXiv.
- Bi-quadratic algebras on 3 generators with PBW: class II.1, arXiv.
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- The group of automorphisms of the algebra of one-sided inverses of a
polynomial algebra.
- The groups of automorphisms of the Lie algebras of formally analytic
vector fields with constant divergence.
- . Journal of Pure and Applied Algebra, 229(1), 107776-107776.
- Research group
- Grants
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Past grants, as Principal Investigator
EPSRC Automorphisms, Derivations and Polynomial Integro-Differential Operators RS
- Teaching activities
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MAS333 Fields MAS438 Fields