Professor Vladimir Bavula

School of Mathematical and Physical Sciences

Professor

v.bavula@sheffield.ac.uk
J15, Hicks Building

Full contact details

Professor Vladimir Bavula
School of Mathematical and Physical Sciences
J15
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
Research interests

Professor 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).

Professor 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

  • Bavula VV (2025) . Journal of Algebra, 677, 745-797.
  • Bavula VV (2025) . Journal of Pure and Applied Algebra, 229(2).
  • Bavula VV (2025) . Journal of Pure and Applied Algebra, 229(1), 107776-107776.
  • Bavula V (2025) . Glasgow Mathematical Journal, 67(1), 67-71.
  • Bavula VV (2024) . Algebras and Representation Theory, 27, 2389-2422.
  • Bavula VV (2024) . Comptes Rendus Math矇matique, 362(G7), 731-738.
  • Bavula VV (2024) . Journal of Noncommutative Geometry, 18(3), 1041-1079.
  • Bavula V & Hakami K (2024) . Algebra and Discrete Mathematics, 38(2), 127-157.
  • Bavula VV (2024) . Journal of Algebra and Its Applications, 23(8).
  • Bavula VV (2024) . Journal of Algebra and Its Applications, 23(13).
  • BAVULA VV (2023) . Tokyo Journal of Mathematics, 46(1).
  • Bavula VV (2023) . Journal of Algebra, 631, 695-730.
  • Bavula V, Bezushchak O, Bondarenko I, Dlab V, Drozd Y, Futorny V, Grigorchuk R, Haiduk V, Kurdachenko L, Lyubashenko V , Maksymenko S et al (2023) Vitaliy M. Bondarenko To the 75th anniversary. ALGEBRA AND DISCRETE MATHEMATICS, 36(1), C-J.
  • Bavula VV (2022) . Journal of Algebra, 610, 38-75.
  • Bavula VV (2022) . Mathematics in Computer Science, 16(1).
  • Bavula VV (2022) . Glasgow Mathematical Journal, 64(2), 347-351.
  • Bavula VV (2021) .
  • Bavula VV (2021) .
  • Alsuraiheed T & Bavula VV (2021) . Journal of Algebra, 584, 69-88.
  • Bavula VV (2021) .
  • Bavula VV (2021) .
  • Bavula VV (2021) .
  • Bavula VV (2021) .
  • Bavula V & Lu T (2021) . Algebra and Discrete Mathematics, 31(1), 1-16.
  • Bavula VV, Bekkert V & Futorny V (2021) . Asian Journal of Mathematics, 25(5), 727-756.
  • Bavula VV & Lu T (2020) . Glasgow Mathematical Journal, 62(S1), S77-S98.
  • (2020) . Communications in Algebra, 48(10), 4554-4554.
  • Bavula VV (2020) . Mathematics in Computer Science, 14, 317-325.
  • Bavula VV (2020) . Mathematics in Computer Science, 14, 339-346.
  • Bavula VV & Levandovskyy V (2020) . Canadian Mathematical Bulletin, 63(1), 6-12.
  • Bavula VV (2020) . Journal of Algebra and Its Applications, 19(02).
  • Bavula VV (2020) . Letters in Mathematical Physics, 110, 105-119.
  • Bavula VV (2019) . Journal of Algebra and Its Applications.
  • Bavula V & Futorny V (2019) . Communications in Algebra, 47(10), 4114-4124.
  • Alsuraiheed T & Bavula VV (2019) . Communications in Algebra, 47(11), 4533-4540.
  • Bavula V, Bekkert V, Bezushchak O, Bondarenko V, Bondarenko I, Burban I, Futorny V, Grigorchuk R, Kurdachenko L, Lavrenyuk Y , Lyubashenko V et al (2019) Yuriy Drozd (dedicated to 75th Birthday). ALGEBRA AND DISCRETE MATHEMATICS, 28(2), C-F.
  • Bavula VV, Bezushchak OO, Bondarenko VM, Dokuchaev MA, Drozd YA, Futorny VM, Ganiushkin OG, Grigorchuk RI, Gubareni NM, Horodnii MF , Kashu AI et al (2019) VOLODYMYR KYRYCHENKO (dedicated to the 75th anniversary). ALGEBRA AND DISCRETE MATHEMATICS, 27(1).
  • Bavula VV & Lu T (2018) . Canadian Mathematical Bulletin, 61(4), 688-703.
  • Bavula VV & Lu T (2018) . Journal of Noncommutative Geometry, 12(3), 889-946.
  • Bavula VV (2018) . Algebras and Representation Theory, 21(2), 359-373.
  • Bavula V, Bekkert V & Futorny V (2018) . Proceedings of the American Mathematical Society, 146, 2373-2380.
  • Bavula VV & Lu T (2018) 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.
  • Bavula VV & Akcin HMT (2018) . Communications in Algebra, 46(4), 1447-1463.
  • Bavula VV (2018) . Journal of Pure and Applied Algebra, 222(7), 1548-1564.
  • Bavula VV & Lu T (2018) . Canadian Mathematical Bulletin, 61(1), 16-39.
  • Bavula VV (2017) . Mathematics in Computer Science, 11(3-4), 253-268.
  • Bavula VV & Lu T (2017) . Israel Journal of Mathematics, 219(2), 929-958.
  • Bavula VV (2017) . Communications in Algebra, 45(3), 1114-1133.
  • Bavula VV & Lu T (2017) . Journal of Mathematical Physics, 58(1).
  • Bavula VV (2017) . Publicationes Mathematicae Debrecen, 90(1-2), 55-90.
  • Bavula V, Bezushchak O, Bekkert V, Bondarenko V, Burban I, Chernikov M, Drozd Y, Ganyushkin A, Grigorchuk R, Futorny V , Kirichenko V et al (2017) Sergiy Ovsienko (01.05.1953-25.01.2016). ALGEBRA AND DISCRETE MATHEMATICS, 23(1), C-F.
  • Bavula VV & Lu T (2017) . Communications in Algebra, 45(10), 4166-4189.
  • Bavula VV (2016) . Journal of Algebra and Its Applications, 16(1750103).
  • Bavula VV (2014) Left localizable rings and their characterizations.
  • Bavula VV (2014) Left localizations of left Artinian rings.
  • Bavula VV (2014) . Journal of Pure and Applied Algebra, 218(5), 829-851.
  • Bavula VV (2013) The group of automorphisms of the Lie algebra of derivations of a field of rational functions.
  • Bavula VV (2013) The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras.
  • Bavula VV (2013) The group of automorphisms of the Lie algebra of derivations of a polynomial algebra.
  • Bavula VV (2013) The largest strong left quotient ring of a ring.
  • Bavula VV (2013) New criteria for a ring to have a semisimple left quotient ring.
  • Bavula VV (2013) The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence.
  • Bavula VV (2013) . Journal of Pure and Applied Algebra, 217(3), 495-529.
  • 訄赲郅訄 & Bavula VV (2013) . 郱赲迮邽 郋邽邿郕郋邿 訄郕訄迡迮邾邽邽 郇訄郕. 苤迮邽 邾訄迮邾訄邽迮郕訄, 77(6), 3-44.
  • Bavula VV (2012) Characterizations of left orders in left Artinian rings.
  • Bavula VV (2012) Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras.
  • Bavula VV (2012) . Comptes Rendus Mathematique, 350(11-12), 553-556.
  • Bavula VV (2012) Every monomorphism of the Lie algebra of unitriangular polynomial derivations is an automorphism.
  • Bavula VV (2012) . Journal of K Theory, 10(3), 583-601.
  • Bavula VV (2011) The largest left quotient ring of a ring.
  • Bavula VV (2011) The algebra of polynomial integro-differential operators is a holonomic bimodule over the subalgebra of polynomial differential operators.
  • Bavula VV (2011) . Journal of Algebra, 348(1), 233-263.
  • Bavula VV (2011) On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra.
  • Bavula VV (2011) The group of automorphisms of the Jacobian algebra An. Journal of Pure and Applied Algebra.
  • Bavula VV (2010) An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators.
  • Bavula VV (2010) An analogue of Hilbert's Syzygy Theorem for the algebra of one-sided inverses of a polynomial algebra.
  • Bavula VV (2010) The algebra of integro-differential operators on an affine line and its modules.
  • Bavula VV (2010) . Algebras and Representation Theory, 13(2), 159-187.
  • Bavula VV (2010) . Journal of Algebra, 323(4), 1036-1051.
  • Bavula VV (2010) The Jacobian map, the Jacobian group and the group of automorphisms of the Grassmann algebra. Bulletin de la Soci矇t矇 Math矇matique de France, 138, 39-117.
  • Bavula VV (2009) The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II.
  • Bavula VV (2009) The algebra of integro-differential operators on a polynomial algebra.
  • Bavula VV (2009) The algebra of one-sided inverses of a polynomial algebra.
  • Bavula VV (2009) The group of automorphisms of the algebra of polynomial integro-differential operators.
  • Bavula VV (2009) . Representation Theory - An electronic journal of the AMS, 13, 182-227.
  • Bavula VV (2008) Extensions of the Frobenius to ring of differential operators on polynomial algebra in prime characteristic.
  • Bavula VV (2008) The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic.
  • Bavula VV (2008) . Communications in Algebra, 36(6), 2195-2201.
  • Bavula VV (2007) Derivations and skew derivations of the Grassmann algebras.
  • Bavula VV (2007) Generalizations of two theorems of Ritt on decompositions of polynomial maps.
  • Bavula VV (2007) The Jacobian algebras.
  • Bavula VV (2007) The group of automorphisms of the first Weyl algebra in prime characteristic and the restriction map.
  • Bavula VV (2007) Primary Decompositions for Left Noetherian Rings.
  • Bavula VV (2007) Factorization of monomorphisms of a polynomial algebra in one variable.
  • Bavula VV & Lenagan TH (2006) Quadratic and cubic invariants of unipotent affine automorphisms.
  • Bavula VV (2006) The inversion formulae for automorphisms of polynomial algebras and differential operators in prime characteristic.
  • Bavula VV & Hinchcliffe V (2006) Morita invariance of the filter dimension and of the inequality of Bernstein.
  • Bavula VV (2006) Simple derivations of differentiably simple Noetherian commutative rings in prime characteristic.
  • Bavula VV (2006) Generators and defining relations for ring of invariants of commuting locally nilpotent derivations or automorphisms.
  • BAVULA VV (2005) . Journal of Algebra and Its Applications, 04(05), 577-586.
  • Bavula VV (2005) The Carlitz Algebras.
  • Bavula VV (2005) The inversion formula for automorphisms of the Weyl algebras and polynomial algebras.
  • Bavula V (2005) Filter Dimension.
  • Bavula VV (2005) . Annali Dell Universita Di Ferrara, 51(1), 1-14.
  • Bavula V (2005) Gelfand-Kirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras. J REINE ANGEW MATH, 582, 61-85.
  • Bavula V (2005) . J PURE APPL ALGEBRA, 199(1-3), 1-10.
  • Bavula V (2005) Solutions to two questions about the Weyl algebras. P AM MATH SOC, 133(6), 1587-1591.
  • Bavula V (2004) Dixmier's Problem 6 for the Weyl Algebra (the Generic type Problem).
  • Bavula VV (2004) Dixmier's Problem 5 for the Weyl Algebra.
  • Bavula V & van Oystaeyen F (2004) . J ALGEBRA, 271(2), 827-845.
  • Bavula VV & Lenagan TH (2001) . Journal of Algebra, 239(1), 93-111.
  • Bavula V & Van Oystaeyen F (2001) Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2. T AM MATH SOC, 353(6), 2193-2214.
  • Bavula VV (2001) . Annals of Mathematics, 154(3), 683-702.
  • Bavula VV & Lenagan TH (2001) . Journal of Algebra, 235(1), 315-358.
  • Bavula VV (2000) . Bulletin of the London Mathematical Society, 32(2), 182-190.
  • Bavula V & Bekkert V (2000) Indecomposable representations of generalized Weyl algebras. COMMUN ALGEBRA, 28(11), 5067-5100.
  • Bavula VV & Jordan DA (2000) Isomorphism problems and groups of automorphisms for generalized Weyl algebras. T AM MATH SOC, 353(2), 769-794.
  • Bavula V & van Oystaeyen F (2000) The simple modules of the Lie superalgebra osp(1,2). J PURE APPL ALGEBRA, 150(1), 41-52.
  • Bavula V & van Oystaeyen F (2000) Simple holonomic modules over the second Weyl algebra A(2). ADV MATH, 150(1), 80-116.
  • Bavula VV & Lenagan TH (1999) . Proceedings of the Edinburgh Mathematical Society, 42(2), 311-332.
  • Bavula V (1999) The simple modules of the ore extensions with coefficients from a Dedekind ring. COMMUN ALGEBRA, 27(6), 2665-2699.
  • Bavula V & van Oystaeyen F (1998) Krull dimension of generalized Weyl algebras and iterated skew polynomial rings: Commutative coefficients. J ALGEBRA, 208(1), 1-34.
  • Bavula V (1998) Krull, Gelfand-Kirillov, and filter dimensions of simple affine algebras. J ALGEBRA, 206(1), 33-39.
  • Bavula V & vanOystaeyen F (1997) The simple modules of certain generalized crossed products. J ALGEBRA, 194(2), 521-566.
  • Bavula VV (1996) . Izvestiya Mathematics, 60(5), 877-885.
  • Bavula VV (1996) . Ukrainian Mathematical Journal, 48(5), 643-651.
  • 訄赲郅訄 & Bavula VV (1996) . 郱赲迮邽 郋邽邿郕郋邿 訄郕訄迡迮邾邽邽 郇訄郕. 苤迮邽 邾訄迮邾訄邽迮郕訄, 60(5), 3-12.
  • Bavula V (1996) Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras. B SCI MATH, 120(3), 293-335.
  • Bavula V (1996) Filter dimension of algebras and modules, a simplicity criterion of generalized Weyl algebras. COMMUN ALGEBRA, 24(6), 1971-1992.
  • BAVULA V (1995) EACH SCHURIAN ALGEBRA IS TENSOR-SIMPLE. COMMUN ALGEBRA, 23(4), 1363-1367.
  • BAVULA VV (1995) 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.
  • Bavula VV (1993) . Ukrainian Mathematical Journal, 45(9), 1327-1338.
  • Bavula VV (1993) . Ukrainian Mathematical Journal, 45(3), 329-334.
  • Bavula VV (1993) . Ukrainian Mathematical Journal, 45(2), 223-234.
  • Bavula VV (1992) . Ukrainian Mathematical Journal, 44(12), 1500-1511.
  • Bavula VV (1992) . Functional Analysis and Its Applications, 26(1), 45-46.
  • Bavula VV (1991) . Functional Analysis and Its Applications, 25(3), 229-230.
  • Bavula VV (1990) . Ukrainian Mathematical Journal, 42(9), 1044-1049.
  • Bavula VV (1990) . Ukrainian Mathematical Journal, 42(7), 873-875.
  • TARTAKOVSKII VK, BAVULA VV & ISUPOV VY (1989) EXCITATION OF NUCLEAR-LEVELS OF ANOMALOUS ROTATIONAL BAND AT THE DIFFRACTIONAL SCATTERING OF NEUTRONS. IZV VUZ FIZ+, 32(8), 107-108.
  • Bavula VV () . Journal of Algebra and Its Applications.
  • Bavula V () . Proceedings of the American Mathematical Society.
  • Bavula VV () . Communications in Algebra, 45(9), 3798-3815.
  • Bavula V () . Banach Center Publications, 40(1), 193-201.

Book chapters

  • Bavula V & Lu T (2019) (pp. 49-70). American Mathematical Society
  • Bavula V (2006) , HANDBOOK OF ALGEBRA, VOL 4 (pp. 77-105).
  • ()

Conference proceedings

  • Bavula VV & Alnefaie K (2020) . CATEGORICAL, HOMOLOGICAL AND COMBINATORIAL METHODS IN ALGEBRA, Vol. 751 (pp 33-60)
  • Bavula VV (2016) . Contemporary Mathematics, Vol. 673 (pp 1-24). Woods Hole Oceanographic Institute, Woods Hole, MA, 1 May 2014 - 1 May 2014.
  • Bavula VV (2005) The ${rm Jacobian Conjecture}_{2n}$ implies the ${rm Dixmier Problem}_n$
  • Bavula V (2000) Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions. INFINITE LENGTH MODULES (pp 149-166)

Working papers

  • Bavula VV (2009) The group of automorphisms of the Jacobian algebra $mA_n$.
  • Bavula VV (2009) ${rm K}_1(mS_1)$ and the group of automorphisms of the algebra $mS_2$ of one-sided inverses of a polynomial algebra in two variables.
  • Bavula VV (2005) Finite generation of division subalgebras and of the group of eigenvalues for commuting derivations or automorphisms of division algebras.

Preprints

  • Bavula VV (2024) , arXiv.
  • Bavula VV (2024) , arXiv.
  • Bavula VV (2024) , arXiv.
  • Bavula V (2023) , arXiv.
  • Bavula V (2023) , arXiv.
  • Bavula V (2023) , arXiv.
  • Bavula V (2023) , arXiv.
  • Bavula V & Khabyah AA (2023) , arXiv.
  • Bavula V (2023) , arXiv.
  • Bavula V & Hakami K (2023) , arXiv.
  • Bavula VV (2022) , arXiv.
  • Bavula VV (2019) , arXiv.
  • Bavula VV (2019) , arXiv.
  • Bavula VV & Levandovskyy V (2018) , arXiv.
  • Bavula VV (2017) , arXiv.
  • Bavula V & Futorny V (2017) , arXiv.
  • Bavula V, Bekkert V & Futorny V (2016) , arXiv.
  • Bavula VV (2016) , arXiv.
  • Bavula VV & Lu T (2015) , arXiv.
  • Bavula VV (2015) , arXiv.
  • Bavula VV (2015) , arXiv.
  • Bavula VV (2014) , arXiv.
  • Bavula VV (2014) , arXiv.
  • Bavula VV (2014) , arXiv.
  • Bavula VV (2013) The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) , arXiv.
  • Bavula VV (2013) The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra.
  • Bavula VV (2012) , arXiv.
  • Bavula VV (2012) , arXiv.
  • Bavula VV (2012) , arXiv.
  • Bavula VV (2012) , arXiv.
  • Bavula VV (2011) , arXiv.
  • Bavula VV (2011) , arXiv.
  • Bavula VV (2011) , arXiv.
  • Bavula VV (2010) , arXiv.
  • Bavula VV (2010) , arXiv.
  • Bavula VV (2010) , arXiv.
  • Bavula VV (2010) , arXiv.
  • Bavula VV (2009) , arXiv.
  • Bavula VV (2009) , arXiv.
  • Bavula VV (2009) , arXiv.
  • Bavula VV (2009) , arXiv.
  • Bavula VV (2009) , arXiv.
  • Bavula VV (2008) , arXiv.
  • Bavula VV (2008) , arXiv.
  • Bavula VV (2008) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV (2007) , arXiv.
  • Bavula VV & Hinchcliffe V (2006) , arXiv.
  • Bavula VV & Lenagan TH (2006) , arXiv.
  • Bavula VV (2006) , arXiv.
  • Bavula VV (2006) , arXiv.
  • Bavula VV (2006) , arXiv.
  • Bavula VV (2006) , arXiv.
  • Bavula VV (2005) , arXiv.
  • Bavula VV (2005) , arXiv.
  • Bavula V (2005) , arXiv.
  • Bavula VV (2005) , arXiv.
  • Bavula VV (2005) , arXiv.
  • Bavula VV (2004) , arXiv.
  • Bavula V (2004) , arXiv.
  • Bavula V (2004) , arXiv.
Research group

Pure Mathematics cluster

Grants

Past grants, as Principal Investigator

 
EPSRC
Automorphisms, Derivations and Polynomial Integro-Differential OperatorsRS
Teaching activities
MAS333Fields
MAS438Fields