Alexandre Mikhailovich Vinogradov (obituary)
- Authors: Astashov A.M., Astashova I.V., Bocharov A.V., Buchstaber V.M., Vassiliev V.A., Verbovetsky A.M., Vershik A.M., Veselov A.P., Vinogradov M.M., Vitagliano L., Vitolo R.F., Voronov T.T., Kac V.G., Kosmann-Schwarzbach Y., Krasil'shchik I.S., Krichever I.M., Krishchenko A.P., Lando S.K., Lychagin V.V., Marvan M., Maslov V.P., Mishchenko A.S., Novikov S.P., Rubtsov V.N., Samokhin A.V., Sosinskii A.B., Stasheff J., Fuchs D.B., Helemskii A.Y., Khor'kova N.G., Chetverikov V.N., Schwarz A.S.
- Issue: Vol 75, No 2 (2020)
- Pages: 185-190
- Section: Articles
- URL: https://journals.rcsi.science/0042-1316/article/view/133605
- DOI: https://doi.org/10.4213/rm9931
- ID: 133605
Cite item
Abstract
About the authors
A. M. Astashov
Irina Viktorovna Astashova
Doctor of physico-mathematical sciences, Professor
Aleksei Vadimovich Bocharov
Candidate of physico-mathematical sciences
Victor Matveevich Buchstaber
Email: buchstab@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
Victor Anatolievich Vassiliev
Email: vva@mi-ras.ru
Doctor of physico-mathematical sciences, no status
Alexander Moiseevich Verbovetsky
Email: alik@ejik.org
Candidate of physico-mathematical sciences, no status
Anatolii Moiseevich Vershik
Email: avershik@gmail.com
Doctor of physico-mathematical sciences, Professor
Aleksandr Petrovich Veselov
Email: A.P.Veselov@lboro.ac.uk
Doctor of physico-mathematical sciences, Professor
Michael M.. Vinogradov
Candidate of physico-mathematical sciences
L. Vitagliano
Email: lvitagliano@unisa.it
R. F. Vitolo
Email: raffaele.vitolo@unile.it
Theodore Theodorovich Voronov
Email: theodore.voronov@manchester.ac.uk
Candidate of physico-mathematical sciences, no status
Victor Gershevich Kac
Email: kac@math.mit.edu
Yvette Kosmann-Schwarzbach
Email: Yvette.Kosmann-Schwarzbach@math.cnrs.fr
Iosif Semenovich Krasil'shchik
Email: josephkra@gmail.com
Doctor of physico-mathematical sciences, Professor
Igor Moiseevich Krichever
Email: krichev@math.columbia.edu
Doctor of physico-mathematical sciences, Professor
Alexander Petrovich Krishchenko
Email: apkri@bmstu.ru
Doctor of physico-mathematical sciences, Professor
Sergei Konstantinovich Lando
Email: lando@mccme.ru
Doctor of physico-mathematical sciences
Valentin Vasil'evich Lychagin
Email: lychagin@math.uit.no
Doctor of physico-mathematical sciences, Professor
Michal Marvan
Email: M.Marvan@math.slu.cz
Victor Pavlovich Maslov
Email: v.p.maslov@mail.ru
Doctor of physico-mathematical sciences, Professor
Alexandr Sergeevich Mishchenko
Email: asmish@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
Sergei Petrovich Novikov
Email: snovikov@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
Vladimir Nikolaevich Rubtsov
Email: volodya@univ-angers.fr
Candidate of physico-mathematical sciences, Professor
Alexey Vasilyevich Samokhin
Email: samohinalexey@gmail.com
Doctor of technical sciences, Associate professor
Aleksei Bronislavovich Sosinskii
Candidate of physico-mathematical sciences
J. Stasheff
Email: jds@math.upenn.edu
Dmitrii Borisovich Fuchs
Email: fuchs@math.ucdavis.edu
Alexander Yakovlevich Helemskii
Nina Grigor'evna Khor'kova
Candidate of physico-mathematical sciences, Associate professor
Vladimir Nikolaevitch Chetverikov
Email: chetveri@diffiety.ac.ru
Candidate of physico-mathematical sciences, Associate professor
Albert S. Schwarz
Doctor of physico-mathematical sciences, Professor
References
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- R. L. Bryant, P. A. Griffiths, “Characteristic cohomology of differential systems. I. General theory”, J. Amer. Math. Soc., 8:3 (1995), 507–596
- A. Verbovetsky, “Notes on the horizontal cohomology”, Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, 211–231
- T. Tsujishita, “On variation bicomplexes associated to differential equations”, Osaka Math. J., 19:2 (1982), 311–363
- J. Stasheff, “The (secret?) homological algebra of the Batalin–Vilkovisky approach”, Secondary calculus and cohomological physics (Moscow, 1997), Contemp. Math., 219, Amer. Math. Soc., Providence, RI, 1998, 195–210
- А. М. Виноградов, “Объединение скобок Схоутена и Нийенхейса, когомологии и супердифференциальные операторы”, Матем. заметки, 47:6 (1990), 138–140
- A. Cabras, A. M Vinogradov, “Extensions of the Poisson bracket to differential forms and multi-vector fields”, J. Geom. Phys., 9:1 (1992), 75–100
- Y. Kosmann-Schwarzbach, “From Poisson algebras to Gerstenhaber algebras”, Ann. Inst. Fourier (Grenoble), 46:5 (1996), 1243–1274
- P. W. Michor, A. M. Vinogradov, “$n$-ary Lie and associative algebras”, Geometrical structures for physical theories. II (Vietri, 1996), Rend. Sem. Mat. Univ. Politec. Torino, 54:4 (1996), 373–392
- G. Marmo, G. Vilasi, A. M. Vinogradov, “The local structure of $n$-Poisson and $n$-Jacobi manifolds”, J. Geom. Phys., 25:1-2 (1998), 141–182
- A. M. Vinogradov, M. M. Vinogradov, “Graded multiple analogs of Lie algebras”, Acta Appl. Math., 72:1-2 (2002), 183–197
- А. М. Виноградов, Е. М. Воробьев, “Применение симметрии для нахождения точных решений уравнения Заболотской–Хохлова”, Акустич. журн., 22:1 (1976), 23–27
- V. N. Gusyatnikova, A. V. Samokhin, V. S. Titov, A. M. Vinogradov, V. A. Yumaguzhin, “Symmetries and conservation laws of Kadomtsev–Pogutse equations (their computation and first applications)”, Acta Appl. Math., 15:1-2 (1989), 23–64
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Vacuum Einstein metrics with bidimensional Killing leaves. I. Local aspects”, Differential Geom. Appl., 16:2 (2002), 95–120
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Vacuum Einstein metrics with bidimensional Killing leaves. II. Global aspects”, Differential Geom. Appl., 17:1 (2002), 15–35
- G. Sparano, G. Vilasi, A. M. Vinogradov, “Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries”, Phys. Lett. B, 513:1-2 (2001), 142–146
- A. M. Vinogradov, “Particle-like structure of Lie algebras”, J. Math. Phys., 58:7 (2017), 071703, 49 pp.
- A. M. Vinogradov, “Particle-like structure of coaxial Lie algebras”, J. Math. Phys., 59:1 (2018), 011703, 42 pp.
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