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Vavilov Nikolay Aleksandrovich

Statistics Math-Net.Ru
Total publications: 83
Scientific articles: 79
Cited articles: 67
Citations in Math-Net.Ru: 510
Presentations: 13

Number of views:
This page:11956
Abstract pages:15612
Full texts:4928
References:1089
Professor
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords: algebraic groups, Chevalley groups, exceptional groups, classical groups, representation theory, algebraic K-theory, Lie algebras, Hopf algebras, associative and non-associative rings, rings, exceptional objects in algebra and geometry, arithmetic groups, presentations of groups, finite groups and geometries, computer algebra and symbolic computation, multilinear algebra, algebraic geometry, algebraic number theory.

Subject:

Structure theory and representations of algebraic groups, algebraic K-theory, overgroups of semisimple groups and tori.

Biography

Zum sehen geboren, zum schauen bestellt

   
Main publications:
  1. A.Stepanov, N.Vavilov, “Decomposition of transvections: a theme with variations”, K-theory, 19 (2000), 109–153
  2. N.Vavilov, “A third look at weight diagrams”, Rendiconti del Seminario Matematico dell'Universitá di Padova, 104 (2000), 201–250
  3. A.Bak, N.Vavilov, “Structure of hyperbolic unitary groups. I. Elementary subgroups”, Algebra Colloquium, 7:2 (2000), 159–196
  4. A.Bak, N.Vavilov, “Presenting powers of augmentation ideal and quadratic forms”, K-theory, 20 (2000), 299–309
  5. R.Hazrat, N.Vavilov, “$K_1$ of Chevalley groups are nilpotent”, J. Pure Appl. Algebra, 179 (2003), 99–116

http://www.mathnet.ru/eng/person21987
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:vavilov.nikolai-a
http://www.ams.org/mathscinet/search/author.html?return=viewitems&mrauthid=189570

Publications in Math-Net.Ru
1. The commutators of classical groups
R. Hazrat, N. Vavilov, Z. Zhang
Zap. Nauchn. Sem. POMI, 443 (2016),  151–221
2. Normaliser of the Chevalley group of type $\mathrm E_7$
N. A. Vavilov, A. Yu. Luzgarev
Algebra i Analiz, 27:6 (2015),  57–88
3. Calculations in exceptional groups, an update
A. Luzgarev, N. Vavilov
Zap. Nauchn. Sem. POMI, 432 (2015),  177–195
4. Decomposition of unipotents for $\mathrm E_6$ and $\mathrm E_7$: 25 years after
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 430 (2014),  32–52
5. The yoga of commutators: further applications
R. Hazrat, A. V. Stepanov, N. A. Vavilov, Z. Zhang
Zap. Nauchn. Sem. POMI, 421 (2014),  166–213
6. Long root tori in Chevalley groups
N. A. Vavilov, A. A. Semenov
Algebra i Analiz, 24:3 (2012),  22–83
7. Overgroups of subsystem subgroups in exceptional groups: levels
N. A. Vavilov, A. V. Shchegolev
Zap. Nauchn. Sem. POMI, 400 (2012),  70–126
8. Parabolic subgroups of $\mathrm{SO}_{2l}$ over a Dedekind ring of arithmetic type
K. O. Batalkin, N. A. Vavilov
Zap. Nauchn. Sem. POMI, 400 (2012),  50–69
9. An $\mathrm A_3$-proof of the structure theorems for Chevalley groups of types $\mathrm E_6$ and $\mathrm E_7$. II. The main lemma
N. A. Vavilov
Algebra i Analiz, 23:6 (2011),  1–31
10. Overgroups of $E(m,R)\otimes E(n,R)$. I
A. S. Ananyevskiy, N. A. Vavilov, S. S. Sinchuk
Algebra i Analiz, 23:5 (2011),  55–98
11. Parabolic factorizations of split classical groups
N. A. Vavilov, S. S. Sinchuk
Algebra i Analiz, 23:4 (2011),  1–30
12. Linear groups over general rings. I. Generalities
N. A. Vavilov, A. V. Stepanov
Zap. Nauchn. Sem. POMI, 394 (2011),  33–139
13. $\mathrm{SL}_2$-factorisations of Chevalley groups
N. A. Vavilov, E. I. Kovach
Zap. Nauchn. Sem. POMI, 394 (2011),  20–32
14. Unitriangular factorisations of Chevalley groups
N. A. Vavilov, A. V. Smolensky, B. Sury
Zap. Nauchn. Sem. POMI, 388 (2011),  17–47
15. The yoga of commutators
R. Hazrat, A. Stepanov, N. Vavilov, Z. Zhang
Zap. Nauchn. Sem. POMI, 387 (2011),  53–82
16. Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation
N. A. Vavilov, A. Yu. Luzgarev
Zap. Nauchn. Sem. POMI, 386 (2011),  5–99
17. The structure of isotropic reductive groups
N. A. Vavilov
Tr. Inst. Mat., 18:1 (2010),  15–27
18. Dennis–Vaserstein type decompositions
N. A. Vavilov, S. S. Sinchuk
Zap. Nauchn. Sem. POMI, 375 (2010),  48–60
19. More variations on decomposition of transvections
N. A. Vavilov, V. G. Kazakevich
Zap. Nauchn. Sem. POMI, 375 (2010),  32–47
20. Some more exceptional numerology
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 375 (2010),  22–31
21. Parabolic subgroups of $\mathrm{SL}_n$ and $\mathrm{Sp}_{2l}$ over a Dedekind ring of arithmetic type
A. V. Alexandrov, N. A. Vavilov
Zap. Nauchn. Sem. POMI, 375 (2010),  5–21
22. Calculations in exceptional groups over rings
N. Vavilov, A. Luzgarev, A. Stepanov
Zap. Nauchn. Sem. POMI, 373 (2009),  48–72
23. Decomposition of transvections for automorphisms
N. A. Vavilov, V. G. Kazakevich
Zap. Nauchn. Sem. POMI, 365 (2009),  47–62
24. Overgroups of $E(m,R)\otimes E(n,R)$
A. S. Ananievskiy, N. A. Vavilov, S. S. Sinchuk
Zap. Nauchn. Sem. POMI, 365 (2009),  5–28
25. Numerology of square equations
N. A. Vavilov
Algebra i Analiz, 20:5 (2008),  9–40
26. $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$
N. A. Vavilov, S. I. Nikolenko
Algebra i Analiz, 20:4 (2008),  27–63
27. Weight elements of Chevalley groups
N. Vavilov
Algebra i Analiz, 20:1 (2008),  34–85
28. Geometry of microweight tori
N. A. Vavilov, V. V. Nesterov
Vladikavkaz. Mat. Zh., 10:1 (2008),  10–23
29. The normalizer of Chevalley groups of type $\mathrm{E}_6$
N. A. Vavilov, A. Yu. Luzgarev
Algebra i Analiz, 19:5 (2007),  37–64
30. Can one see the signs of structure constants?
N. A. Vavilov
Algebra i Analiz, 19:4 (2007),  34–68
31. Geometry of 1-tori in $\mathrm{GL}(n,T)$
N. Vavilov
Algebra i Analiz, 19:3 (2007),  119–150
32. Overgroups of $\mathrm{EO}(n,R)$
N. A. Vavilov, V. A. Petrov
Algebra i Analiz, 19:2 (2007),  10–51
33. Basic reductions for the description of normal subgroups
N. A. Vavilov, A. K. Stavrova
Zap. Nauchn. Sem. POMI, 349 (2007),  30–52
34. On subgroups of symplectic group containing a subsystem subgroup
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 349 (2007),  5–29
35. Triples of long root subgroups
N. A. Vavilov, I. M. Pevzner
Zap. Nauchn. Sem. POMI, 343 (2007),  54–83
36. Subgroups of $\operatorname{SL}_n$ over a semilocal ring
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 343 (2007),  33–53
37. Orbits of subsystem stabilisers
N. A. Vavilov, N. P. Kharchev
Zap. Nauchn. Sem. POMI, 338 (2006),  98–124
38. Polyvector representations of $\operatorname{GL}_n$
N. A. Vavilov, E. Ya. Perelman
Zap. Nauchn. Sem. POMI, 338 (2006),  69–97
39. Chevalley group of type $\mathrm E_6$ in the 27-dimensional representation
N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner
Zap. Nauchn. Sem. POMI, 338 (2006),  5–68
40. Structure of Chevalley groups: the proof from the Book
N. A. Vavilov, M. R. Gavrilovich, S. I. Nikolenko
Zap. Nauchn. Sem. POMI, 330 (2006),  36–76
41. $\mathrm A_2$-proof of structure theorem for Chevaller groups of type $\mathrm E_6$ and $\mathrm E_7$
N. A. Vavilov, M. R. Gavrilovich
Algebra i Analiz, 16:4 (2004),  54–87
42. On supergroups of $\mathrm{Ep}(2l,R)$
N. A. Vavilov, V. A. Petrov
Algebra i Analiz, 15:4 (2003),  72–114
43. Variations on a theme of Higman
N. A. Vavilov, V. A. Petrov
Zap. Nauchn. Sem. POMI, 289 (2002),  57–62
44. Subgroups of the spinor group containing a split maximal torus. II
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 289 (2002),  37–56
45. Do it yourself structure constants for Lie algebras of types $\mathrm E_l$
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 281 (2001),  60–104
46. Subgroups of split orthogonal groups over a commutative ring
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 281 (2001),  35–59
47. Overgroups of $\mathrm{EO}(2l,R)$
N. A. Vavilov, V. A. Petrov
Zap. Nauchn. Sem. POMI, 272 (2000),  68–85
48. Subgroups of the split orthogonal group. II
N. A. Vavilov
Zap. Nauchn. Sem. POMI, 265 (1999),  42–63
49. Computational Group Theory in St. Petersburg
N. A. Vavilov, V. I. Mysovskikh, Yu. G. Teterin
Zap. Nauchn. Sem. POMI, 236 (1997),  42–49
50. On subgroups of the spinorial group containing a split maximal torus. I
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 191 (1991),  49–75
51. Subgroups of splittable classical groups
N. A. Vavilov
Trudy Mat. Inst. Steklov., 183 (1990),  29–42
52. Subgroups of the general linear group over a local field
N. A. Vavilov, I. Khamdan
Izv. Vyssh. Uchebn. Zaved. Mat., 1989, no. 12,  8–15
53. Subgroups of the general linear group over a ring that satisfies stability conditions
N. A. Vavilov, A. V. Stepanov
Izv. Vyssh. Uchebn. Zaved. Mat., 1989, no. 10,  19–25
54. Linear groups generated by one-parameter groups of one-dimensional transformations
N. A. Vavilov
Uspekhi Mat. Nauk, 44:1(265) (1989),  189–190
55. Bruhat decomposition for long root tori in Chevalley groups
N. A. Vavilov, A. A. Semjonov
Zap. Nauchn. Sem. LOMI, 175 (1989),  12–23
56. Subgroups of the general linear group over a Dedekind ring of arithmetic type
N. A. Vavilov
Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 12,  14–20
57. Arrangement of subgroups in the general linear group over a commutative ring
Z. I. Borevich, N. A. Vavilov
Trudy Mat. Inst. Steklov., 165 (1984),  24–42
58. Subgroups of the general symplectic group, containing the group of diagonal matrices. II
N. A. Vavilov, E. V. Dybkova
Zap. Nauchn. Sem. LOMI, 132 (1983),  44–56
59. On definition of the net subgroup
Z. I. Borevich, N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 132 (1983),  26–33
60. Arrangement of subgroups containing a group of block diagonal matrices in the general linear group over a ring
Z. I. Borevich, N. A. Vavilov
Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 11,  12–16
61. On subgroups of the unitary group over a semilocal ring
N. A. Vavilov
Uspekhi Mat. Nauk, 37:4(226) (1982),  147–148
62. Parabolic subgroups of Chevalley groups over a commutative ring
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 116 (1982),  20–43
63. Net determinant over a Bezoutian local ring
Z. I. Borevich, N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 116 (1982),  5–13
64. Net subgroups of Chevalley groups. II. Gauss decomposition
N. A. Vavilov, E. B. Plotkin
Zap. Nauchn. Sem. LOMI, 114 (1982),  62–76
65. A Bruhat decomposition for subgroups containing the group of diagonal matrices. II
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 114 (1982),  50–61
66. Determinants in net subgroups
Z. I. Borevich, N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 114 (1982),  37–49
67. Subgroups of the general symplectic group containing the group of diagonal matrices
N. A. Vavilov, E. V. Dybkova
Zap. Nauchn. Sem. LOMI, 103 (1980),  31–47
68. Bruhat decomposition for subgroups containing the group of diagonal matrices
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 103 (1980),  20–30
69. Net subgroups of Chevalley groups
N. A. Vavilov, E. B. Plotkin
Zap. Nauchn. Sem. LOMI, 94 (1979),  40–49
70. Normal structure of the full linear group over a semilocal ring
N. A. Vavilov, L. Yu. Kolotilina
Zap. Nauchn. Sem. LOMI, 94 (1979),  37–39
71. Parabolic subgroups of twisted Chevalley groups over a semilocal ring
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 94 (1979),  21–36
72. Subgroups of the full linear group over a Dedekind ring
Z. I. Borevich, N. A. Vavilov, V. Narkevich
Zap. Nauchn. Sem. LOMI, 94 (1979),  13–20
73. Self-normalizing nilpotent subgroups of the full linear group over a finite field
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 86 (1979),  34–39
74. Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 86 (1979),  30–33
75. Subgroups of the general linear group over a semilocal ring that contain a group of diagonal matrices
Z. I. Borevich, N. A. Vavilov
Trudy Mat. Inst. Steklov., 148 (1978),  43–57
76. Parabolic subgroups of Chevalley groups over a semilocal ring
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 75 (1978),  43–58
77. Subgroups of the full linear group over a semilocal ring
Z. I. Borevich, N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 75 (1978),  32–34
78. Parabolic subgroups of the general linear group over Dedekind domain of arithmetic type
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 71 (1977),  66–79
79. Parabolic congruence subgroups in linear groups
N. A. Vavilov
Zap. Nauchn. Sem. LOMI, 64 (1976),  55–63

80. To the anniversary of Sergei Vladimirovich Vostokov
D. G. Benua, M. V. Bondarko, N. A. Vavilov, M. A. Vsemirnov, A. I. Generalov, N. L. Gordeev, I. B. Zhukov, G. A. Leonov, B. B. Lur'e, I. A. Panin, A. L. Smirnov, I. B. Fesenko, A. V. Yakovlev
Algebra i Analiz, 27:6 (2015),  3–5
81. Koibaev Vladimir Amurkhanovich (on his 60th birthday)
N. A. Vavilov, A. Kh. Zhurtov, A. S. Kondrat'ev, A. G. Kusraev, V. M. Levchuk, V. D. Mazurov, A. A. Makhnev, Ya. N. Nuzhin, U. M. Pachev, B. I. Plotkin, N. S. Romanovskii
Vladikavkaz. Mat. Zh., 17:2 (2015),  68–70
82. Valentin Evgen'evich Voskresenskii (obituary)
N. A. Vavilov, È. B. Vinberg, I. A. Panin, A. N. Panov, A. N. Parshin, V. P. Platonov, V. L. Popov
Uspekhi Mat. Nauk, 69:4(418) (2014),  177–178
83. Anatolii Vladimirovich Yakovlev
N. A. Vavilov, S. V. Vostokov, A. I. Generalov, N. L. Gordeev, B. B. Lur'e, A. S. Merkur'ev, V. V. Ishkhanov, I. A. Panin, A. I. Skopin, A. A. Suslin
Zap. Nauchn. Sem. POMI, 272 (2000),  5–13

Presentations in Math-Net.Ru
1. Structure and K-theory of Chevalley groups over rings
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
June 16, 2016 14:00   
2. Higher composition laws and exceptional groups
St. Petersburg Seminar on Representation Theory and Dynamical Systems
April 13, 2016 14:00
3. Structure of isotropic reductive groups
Algebraic Geometry and Number Theory
June 24, 2014 12:30   
4. New computation methods in exceptional Chevalley groups
Lie groups and invariant theory
October 24, 2012 16:45
5. Higher composition laws and exceptonal groups
Meetings of the St. Petersburg Mathematical Society
May 25, 2010
6. Mathematical proof: yesterday, today, tomorrow
Meetings of the St. Petersburg Mathematical Society
March 23, 2010
7. Конструкции исключительных групп
Homology and homotopy methods in geometry
February 17, 2010
8. Строение изотропных редуктивных групп
Seminar of the Department of Algebra
February 16, 2010 15:00
9. Высшие законы композиции и исключительные группы
Meetings of the Moscow Mathematical Society
February 16, 2010
10. Строение исключительных групп над кольцами
Lie groups and invariant theory
December 24, 2008
11. Calculations in exceptional groups
Meetings of the St. Petersburg Mathematical Society
November 13, 2007
12. Соединить идеи с вычислениями. От Эйлера до компьютерной алгебры
Meetings of the St. Petersburg Mathematical Society
May 16, 2007
13. The $(1+\epsilon)$-generation of finite simple groups and Hurwitz groups
Meetings of the St. Petersburg Mathematical Society
October 5, 1999

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