Vladimir Rubtsov
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Vladimir Rubtsov has a total of 11 co-authors. Here are the top co-authors by number of shared publications:
- Ugo Bruzzo
SISSA (Scuola Internazionale Superiore di Studi Avanzati), Trieste, Italia
5 shared publications - Giovanni Ortenzi
Dipartimento di Matematica “G.Peano”, Università degli studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
4 shared publications - Serge Roméo Tagne Pelap
University of Luxembourg, Mathematics Research Unit, Luxembourg
3 shared publications - A. Silantyev
Moscow reg Laboratory of Theoretical Physics JINR 141980 Dubna Russia
2 shared publications - Stanislav Pakuliak
Laboratory of Theoretical Physics JINR 141980 Dubna Moscow reg Russia
2 shared publications - Yvette Kosmann-Schwarzbach
Centre de Mathématiques Laurent Schwartz École Polytechnique 91128 Palaiseau France
2 shared publications
Latest Publications
- Open Access
- 18 December 2020
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- Vol. 15 (2) , 495-504
Koszul complexes and spectral sequences associated with Lie algebroids
We study some spectral sequences associated with a locally free $${{\mathscr {O}}}_X$$ -module $${{\mathscr {A}}}$$ which has a Lie algebroid structure. HereXis either a complex manifold or a regular scheme over an algebraically closed fieldk. One spectral sequence can be associated with $${{\mathscr {A}}}$$ by choosing a global sectionVof $${{\mathscr {A}}}$$ , and considering a Koszul complex with a differential given by inner product byV. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ of a holomolorphic vector bundle $${{\mathscr {E}}}$$ on a complex manifold. IfVis a differential operator on $${{\mathscr {E}}}$$ with scalar symbol, i.e, a global section of $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ , we associate with the pair $$({{\mathscr {E}}},V)$$ a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted ( $${{\mathscr {E}}}=0$$ ) case.- 18 December 2020
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- Vol. 15 (2) , 495-504
Open AccessKoszul complexes and spectral sequences associated with Lie algebroids
We study some spectral sequences associated with a locally free $${{\mathscr {O}}}_X$$ -module $${{\mathscr {A}}}$$ which has a Lie algebroid structure. HereXis either a complex manifold or a regular scheme over an algebraically closed fieldk. One spectral sequence can be associated with $${{\mathscr {A}}}$$ by choosing a global sectionVof $${{\mathscr {A}}}$$ , and considering a Koszul complex with a differential given by inner product byV. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ of a holomolorphic vector bundle $${{\mathscr {E}}}$$ on a complex manifold. IfVis a differential operator on $${{\mathscr {E}}}$$ with scalar symbol, i.e, a global section of $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ , we associate with the pair $$({{\mathscr {E}}},V)$$ a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted ( $${{\mathscr {E}}}=0$$ ) case. - 2 May 2019
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 141, 159-160
Editors’ preface to the Topical Issue on the Geometry and Algebra of PDEs
- 2 May 2019
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 141, 159-160
Editors’ preface to the Topical Issue on the Geometry and Algebra of PDEs
- Open Access
Lie algebroid cohomology and Lie algebroid extensions
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions 0 --> L --> E --> Q --> 0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.
Open AccessLie algebroid cohomology and Lie algebroid extensions
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions 0 --> L --> E --> Q --> 0, and classify the extensions in terms of a suitable Lie algebroid hypercohomology group. In the preliminary sections we study free Lie algebroids and recall some basic facts about Lie algebroid hypercohomology.
- Open Access
On localization in holomorphic equivariant cohomology
We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.
Open AccessOn localization in holomorphic equivariant cohomology
We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.
- Open Access
Integer solutions of integral inequalities and H-invariant Jacobian Poisson structures
We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors respectively.
Open AccessInteger solutions of integral inequalities and H-invariant Jacobian Poisson structures
We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors respectively.
- 1 December 2010
- Published by Springer Nature in Theoretical and Mathematical Physics
- Vol. 165 (3) , 1598-1609
Cohomology of skew-holomorphic lie algebroids
- 1 December 2010
- Published by Springer Nature in Theoretical and Mathematical Physics
- Vol. 165 (3) , 1598-1609
Cohomology of skew-holomorphic lie algebroids
- 23 October 2010
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 96 (1-3) , 263-284
On the Heisenberg Invariance and the Elliptic Poisson Tensors
- 23 October 2010
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 96 (1-3) , 263-284
On the Heisenberg Invariance and the Elliptic Poisson Tensors
- Open Access
On the Heisenberg invariance and the Elliptic Poisson tensors
We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$ are the main important example. We classify all quadratic $H-$invariant Poisson tensors on ${\mathbb C}^n$ with $n\leq 6$ and show that for $n\leq 5$ they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations.Open AccessOn the Heisenberg invariance and the Elliptic Poisson tensors
We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$ are the main important example. We classify all quadratic $H-$invariant Poisson tensors on ${\mathbb C}^n$ with $n\leq 6$ and show that for $n\leq 5$ they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations. - Open Access
Cohomology of skew-holomorphic Lie algebroids
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
Open AccessCohomology of skew-holomorphic Lie algebroids
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
- 3 February 2009
- Published by Springer Nature in Acta Applicandae Mathematicae
- Vol. 109 (1) , 101-135
Compatible Structures on Lie Algebroids and Monge-Ampère Operators
- 3 February 2009
- Published by Springer Nature in Acta Applicandae Mathematicae
- Vol. 109 (1) , 101-135
Compatible Structures on Lie Algebroids and Monge-Ampère Operators