Nikolai Aleksandrovich Vavilov

E. B. Plotkin ; A. I. Generalov ; N. S. Geldhauser ; N. L. Gordeev ; A. Yu. Luzgarev ; V. V. Nesterov ; I. A. Panin ; V. A. Petrov ; S. Yu. Pilyugin ; A. V. Stepanov ; A. K. Stavrova ; V. G. Khalin

Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 7-40

Bibliographie

[1] A. Ananievskii, N. Vavilov, S. Sinchuk, “Overgroups of $E(l, R) \otimes E(m, R)$”, J. Math. Sci., 161:4 (2009), 461–473 | DOI | MR

[2] M. Aschbacher M., “On the maximal subgroups of the finite classical groups”, Invent. Math., 76:3 (1984), 469–514 | DOI | MR | Zbl

[3] A. Bak, R. Hazrat, N.A. Vavilov, “Localization-completion strikes again: relative K1 is nilpotent by abelian”, J. Pure Appl. Algebra, 213 (2009), 1075–1085 | DOI | MR | Zbl

[4] A. Bak, V. Petrov, Guoping Tang, “Stability for quadratic $K_1$”, K-Theory, 30:1 (2003), 1–11 | DOI | MR | Zbl

[5] A. Bak, N.A. Vavilov, “Structure of hyperbolic unitary groups. I. Elementary subgroups”, Algebra Colloquium, 7:2 (2000), 159–196 | DOI | MR | Zbl

[6] H. Bass, J. Milnor, J-P. Serre, “Solution of the congruence subgroup problem for $SL_n$ $(n \geq 3)$ and $Sp_{2n}$ $(n \geq 2)$”, Publ. Math. IHES, 33 (1967), 59–137 | DOI | MR | Zbl

[7] Z. I. Borewicz, “A description of the subgroups of the general linear group containing the group of diagonal matrices”, J. Sov. Math., 17:2 (1981), 1718–1730 | DOI | Zbl

[8] Z. I. Borewicz, W. Narkiewicz, N. A. Vavilov, “On subgroups of the general linear group over a Dedekind ring”, J. Sov. Math., 19:1 (1982), 982–987 | DOI | MR | Zbl

[9] Z. I. Borewicz, N. A. Vavilov, “Subgroups of the general linear group over a semilocal ring containing the group of diagonal matrices”, Proc. Steklov Inst. Math., 1980, no. 4, 41–54 | MR | Zbl

[10] Z. I. Borewicz, N. A. Vavilov, “On the subgroups of the general linear group over a commutative ring”, Soviet Math. Dokl., 26:3 (1982), 679–681 | MR | Zbl

[11] Z. I. Borewicz, N. A. Vavilov, “The distribution of subgroups in the general linear group over a commutative ring”, Proc. Steklov. Inst. Math., 165:3 (1985), 27–46 | MR | Zbl

[12] L. Di Martino, N.A. Vavilov, “(2; 3)-generation of $SL(n; q)$. I. Cases n = 5; 6; 7”, Commun. Algebra, 1994, 1321–1347 | DOI | MR | Zbl

[13] E. V. Dybkova, N. A. Vavilov, “Subgroups of the general symplectic group, containing the group of diagonal matrices”, J. Sov. Math., 24 (1984), 406–416 | DOI | MR | Zbl

[14] E. V. Dybkova, N. A. Vavilov, “Subgroups of the general symplectic group containing the group of diagonal matrices”, Zap. Nauchn. Semin. LOMI, 103, 1980, 31–47 ; 155–156 | MR | Zbl

[15] E. V. Dybkova, N. A. Vavilov, “Subgroups of the general symplectic group containing the group of diagonal matrices, II”, Zap. Nauchn. Semin. LOMI, 132, 1983, 44–56 | MR

[16] M. Gavrilovich, S. I. Nikolenko, N. A. Vavilov, “Structure of Chevalley groups: the proof from the Book”, J. Math. Sci., 140:5 (2007), 626–645 | DOI | MR

[17] M. Gavrilovich, N. A. Vavilov, “An $A_2$-proof of the structure theorems for Chevalley groups of types $E_6$ and $E_7$”, St. Petersburg Math. J., 16:4 (2005), 649–672 | DOI | MR | Zbl

[18] P. Gvozdevsky, Overgroups of subsysten subgroups, Ph.D. thesis, SPbU, 2023

[19] P. Gvozdevsky, “Overgroups of subsystem subgroups in exceptional groups: nonideal levels”, St. Petersburg Math. J., 33:6 (2022), 897–925 | DOI | MR | Zbl

[20] A. L. Harebov, N. A. Vavilov, “On the lattice of subgroups of Chevalley group containing a split maximal torus”, Commun. Algebra, 34:1 (1996), 103–133 | MR

[21] R. Hazrat, A. Stepanov, N. A. Vavilov, Z. Zhang, “The yoga of commutators”, J. Math. Sci., 179 (2011), 662–678 | DOI | MR | Zbl

[22] R. Hazrat, A. Stepanov, N. A. Vavilov, Z. Zhang, “The yoga of commutators:further applications”, J. Math. Sci., 200:6 (2014), 742–768 | DOI | MR | Zbl

[23] R. Hazrat, A. Stepanov, N. A. Vavilov, Z. Zhang, “Commutator width in Chevalley groups”, Note di Mat., 33:1 (2013), 139–170 | MR | Zbl

[24] R. Hazrat, N. A. Vavilov, “Bak's work on K-theory of rings”, J. Pure Appl. Algebra, 213 (2009), 1075–1085 | DOI | MR | Zbl

[25] R. Hazrat, N. A. Vavilov, “$K_1$ of Chevalley groups are nilpotent”, J. Pure Appl. Algebra, 179 (2003), 99–116 | DOI | MR | Zbl

[26] V. I. Kopeiko, “The stabilization of symplectic groups over a polynomial ring”, Math. U.S.S.R., Sbornik, 34 (1978), 655–669 | DOI | MR | Zbl

[27] B. Kunyavskii, A. Lavrenov, E. Plotkin, N. Vavilov, Bounded generation of Steinberg groups over Dedekind rings of arithmetic type, 2023, 23 pp., arXiv: 2307.05526v2 [math.KT]

[28] B. Kunyavskii , E. Plotkin, N. Vavilov, “Bounded generation and commutator width of Chevalley groups: function case”, European J. Math., 9 (2023), 53 | DOI | MR | Zbl

[29] B. Kunyavskii, E. Plotkin, N.Vavilov, Uniform bounded elementary generation of Chevalley groups, 2023, 30 pp., arXiv: 2307.15756 [math.GR]

[30] A. Lavrenov, S. Sinchuk, “On centrality of even orthogonal $K_2$”, J. Pure Appl. Alg., 221:5 (2017), 1134–1145 | DOI | MR | Zbl

[31] A. Lavrenov, S. Sinchuk, E. Voronetsky, “Centrality of $K_2$ for Chevalley groups: a pro-group approach”, Isr. J. Math., 2024 | MR

[32] R. Lubkov, Overgroups of the elementary subgroups of reductive groups in irreducible representations, Ph.D. thesis, SPbU, 2022 | MR

[33] R. Lubkov, A. Stepanov, “Subgroups of Chevalley groups over rings”, J. Math. Sci., 252 (2021), 829–840 | DOI | MR | Zbl

[34] A. Luzgarev, Overgroups of exceptional groups, PhD thesis, SPbU, Saint-Petersburg, 2008

[35] A. Luzgarev, “On overgroups of $E(E_6, R)$ and $E(E_7, R)$ in their minimal representations”, J. Math. Sci., 134:6 (2004), 2558–2571 | DOI | MR | Zbl

[36] A. Luzgarev, “Overgroups of $F_4$ in $E_6$ over commutative rings”, St.Petersburg Math. J., 20 (2009), 955–981 | DOI | MR | Zbl

[37] A. Luzgarev, A. Stavrova, “Elementary subgroup of an isotropic reductive group is perfect”, St. Petersburg Math. J., 23:5 (2012), 881–890 | DOI | MR | Zbl

[38] A. Luzgarev, N. A. Vavilov, “Calculations in Exceptional Groups, an Update”, J. Math. Sci., 209 (2015), 922–934 | DOI | MR | Zbl

[39] V. V. Nesterov, N. A. Vavilov, “Geometry of microweight tori”, Vladikavkaz J. Math., 10:1 (2008), 10–23 | MR | Zbl

[40] V. V. Nesterov, N. A. Vavilov, “Pairs of microweight tori in $GL_n$”, Chebyshevskii Sbornik, 21:4 (2020), 152–161 | DOI | MR | Zbl

[41] I. Panin, A. Stavrova, N. Vavilov, “On Grothendieck– Serre's conjecture concerning principal-bundles over reductive group schemes”, Compositio Mathematica, 151:3 (2015), 535–567 | DOI | MR | Zbl

[42] V. A. Petrov, “Odd unitary groups”, J. Math. Sci., 130:3 (2005), 475–4766 | MR

[43] V. Petrov. A. Stavrova, “Elementary subgroups in isotropic reductive groups”, St.Petersburg Math. J., 20:4 (2009), 625–644 | DOI | MR | Zbl

[44] V. A. Petrov, N. A. Vavilov, “Overgroups of $Ep(2l;R)$”, St. Petersburg Math. J., 15:4 (2004), 515–543 | DOI | MR | Zbl

[45] V. A. Petrov, N. A. Vavilov, “Overgroups of $EO(n, R)$”, St. Petersburg Math. J., 19:2 (2008), 167–195 | DOI | MR | Zbl

[46] E. Plotkin, A.Semenov, N. A. Vavilov, “Visual basic representations: an atlas”, Int. J. Algebra Comp., 8:1 (1998), 61–95 | DOI | MR | Zbl

[47] E. Plotkin, A. Stepanov, N.A. Vavilov, “Calculations in Chevalley groups over commutative rings”, Soviet. Math. Dokl., 40:1 (1989), 145–147 | MR | Zbl

[48] G. Seitz, The maximal subgroups of classical algebraic groups, Mem. Amer. Math. Soc., 67, no. 365, 1987 | MR

[49] A. Stavrova, Stroenije isotropnyh reduktivnyh grupp, PhD Thesis, St. Petersburg State University, 2009 | Zbl

[50] A. Stavrova, “Homotopy invariance of non-stable $K_1$-functors”, J. K-Theory, 13:2 (2014), 199–248 | DOI | MR | Zbl

[51] A. Stavrova, A. Stepanov, “Normal structure of isotropic reductive groups over rings”, J. Algebra, 2022 | MR

[52] A. V. Shchegolev, Overgroups of elementary block-diagonal subgroups in even unitary groups over quasi-finite rings, Ph.D. thesis, Universität Bielefeld, 2015

[53] A. V. Shchegolev, “Overgroups of an elementary block-diagonal subgroup of the classical symplectic group over an arbitrary commutative ring”, St. Petersburg Math. J., 30:6 (2019), 1007–1041 | DOI | MR | Zbl

[54] S Sinchuk, “On centrality of $K_2$ for Chevalley groups of type $E_l$”, J. Pure Appl. Alg., 220:2 (2016), 857–875 | DOI | MR | Zbl

[55] A. S. Sivatski, A. V. Stepanov, “On the word length of commutators in $GL_n(R)$”, K-Theory, 17:4 (1999), 295–302 | DOI | MR | Zbl

[56] A. Smolensky, B. Sury, N. A. Vavilov, “Gauss decomposition for Chevalley groups, revisited”, Intern. J. Group Theory, 1:1 (2012), 3–16 | MR | Zbl

[57] M. Stein, “Stability theorems for $K1$, $K2$ and related functors modeled on Chevalley groups”, Japan. J. Math., 4 (1978), 77–108 | DOI | MR | Zbl

[58] A. Stepanov, “Free product subgroups between Chevalley groups $G(\Phi, F)$ and $G(\Phi, F[t])$”, J. Algebra, 324:7 (2010), 1549–1557 | DOI | MR | Zbl

[59] A. Stepanov, “Subring subgroups in Chevalley groups with doubly laced root systems”, J. Algebra, 362 (2012), 12–29 | DOI | MR | Zbl

[60] A. Stepanov, N. A. Vavilov, “Decomposition of transvections: a theme with variations”, $K$-theory, 19 (2000), 109–153 | DOI | MR | Zbl

[61] A. Stepanov, N. A. Vavilov, “On the length of commutators in Chevalley groups”, Israel Math. J., 185:1 (2011), 253–276 | DOI | MR | Zbl

[62] A. Stepanov, N. A. Vavilov, “Standard commutator formulae”, Vest. St. Petersburg Univ., Ser. 1, 2008, no. 1, 9–14 | MR | Zbl

[63] Math. USSR-Izv., 11:2 (1977), 22–238 | DOI | MR | Zbl

[64] G. Taddei, “Normalité des groupes eléméntaire dans les groupes de Chevalley sur un anneau”, Contemp. Math., 55, no. 2, 1986, 693–710 | DOI | MR | Zbl

[65] N. A. Vavilov, “Parabolic subgroups of Chevalley groups over a semi-local ring”, J. Sov. Math., 37 (1987), 942–952 | DOI | Zbl

[66] N. A. Vavilov, “On subgroups of split orthogonal groups over a ring”, Siberian Math. J., 29:4 (1988), 537–547 | DOI | MR | Zbl

[67] N. A. Vavilov, “Subgroups of split orthogonal groups”, Siberian Math. J., 29:3 (1988), 341–352 | DOI | MR | Zbl

[68] N. A. Vavilov, “The group $SL_n$ over a Dedekind ring of arithmetic type”, Vestn. Leningrad. Univ. Mat. Mekh. Astronom., 1983, 5–10 | MR | Zbl

[69] N. A. Vavilov, “Subgroups of the general linear group over a ring that satisfies stability conditions”, Izv. Vysh. Uchebnykh Zavedeniĭ. Matematika, 10, 19–25 | MR

[70] N. A. Vavilov, “Subgroups of splittable classical groups”, Transl. Proc. Steklov Inst. Math., 1991, no. 4, 27–41 | MR

[71] N. A. Vavilov, “On subgroups of the spinor group that contain a splittable maximal torus. II”, J. Math. Sci., 124:1 (2004), 4698–4707 | DOI | MR

[72] N. A. Vavilov, “Structure of Chevalley groups over commutative rings”, Proc. Conf. Non-associative algebras and related topics (Hiroshima, 1990), World Scientific, Singapore et al, 1991, 219–335 | MR | Zbl

[73] N. A. Vavilov, “Subgroups of Chevalley groups containing a maximal torus”, Transl. Amer. Math. Soc., 155 (1993), 59–100 | MR | Zbl

[74] N. A. Vavilov, “A third look at weight diagrams”, Rendiconti del Seminario Matematico dell Universita di Padova, 104 (2000), 201–250 | MR | Zbl

[75] N. A. Vavilov, “Do it yourself structure constants for Lie algebras of type $E_l$”, J. Math. Sci., 120:4 (2004), 1513–1548 | DOI | MR

[76] N. A. Vavilov, “An $A_3$-proof of the structure theorems for Chevalley groups of types $E_6$ and $E_7$”, Int. J. Algebra Comput., 17:5–6 (2007), 1283–1298 | DOI | MR | Zbl

[77] N. A. Vavilov, “Decomposition of unipotents for $E_6$ and $E_7$: 25 years after”, J. Math. Sci., 219:3 (2016), 355–369 | DOI | MR | Zbl

[78] N. A. Vavilov, “Numerology of quadratic equations”, St. Petersburg Math. J., 20:5 (2009), 687–707 | DOI | MR | Zbl

[79] N.A. Vavilov, “Some more exceptional numerology”, J. Math. Sci., 171:3 (2010), 317–321 | DOI | MR | Zbl

[80] N. A. Vavilov, “Geometry of 1-tori in $GL_n$”, St. Petersburg Math. J., 19:3 (2008), 407–429 | DOI | MR | Zbl

[81] N. A. Vavilov, “Weight elements of Chevalley groups”, St. Petersburg Math. J., 20:1 (2009), 23–57 | DOI | MR | Zbl

[82] N. A. Vavilov, “The structure of isotropic reductive groups”, Tr. Inst. Mat., 18:1 (2010), 15–27 | Zbl

[83] N. A. Vavilov, “Reshaping the metaphor of proof”, Philos. Trans. Roy. Soc. A, 377:2140 (2019), 20180279, 18 pp. | DOI | MR | Zbl

[84] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. I. Personal account”, Kompyuternye instrumenty v obrazovanii, 2020, no. 2, 5–26

[85] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. II. Problema Varinga”, Kompyuternye instrumenty v obrazovanii, 2020, no. 3, 5–55

[86] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. III. Chisla Mersenna i summy delitelei”, Kompyuternye instrumenty v obrazovanii, 2020, no. 4, 5–58

[87] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. IV. Problema Goldbakha”, Kompyuternye instrumenty v obrazovanii, 2021, no. 4, 5–71

[88] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. V. Legkaya problema Varinga”, Kompyuternye instrumenty v obrazovanii, 2022, no. 3, 5–63

[89] N. A. Vavilov, “Kompyuter kak novaya realnost matematiki. VI. Chisla Ferma i ikh rodstvenniki”, Kompyuternye instrumenty v obrazovanii, 2022, no. 4, 5–67

[90] N. A. Vavilov, “Sankt-Peterburgskaya shkola teorii lineinykh grupp. I. Predystoriya”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 10 (68):3 (2023), 381–405 | Zbl

[91] N. A. Vavilov, “Sankt-Peterburgskaya shkola teorii lineinykh grupp. II. Rannie raboty Suslina”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 11 (69):1 (2024), 48–83 | Zbl

[92] N. A. Vavilov, V. G. Khalin, A. V. Yurkov, “The Skies Are Falling: Mathematics for Non-Mathematicians”, Dokl. Math., 107, Suppl 1 (2023), S137–S150 | DOI | MR

[93] N. A. Vavilov, V. G. Khalin, A. V. Yurkov, Mathematica dlya nematematika, uchebnoe posobie dlya vuzov, Elektronnoe izdanie, MTsNMO, M., 2021, 483 pp. https://www.mccme.ru/free-books/mathematica.pdf

[94] N. A. Vavilov, N. P. Kharchev, “Orbits of subsystem stabilisers”, Zap. Nauch. Semin. POMI, 338, 2006, 98–124 | MR | Zbl

[95] N. Vavilov, A. Luzgarev, A. Stepanov, “Calculations in exceptional groups over rings”, J. Math. Sci., 168:3 (2010), 334–348 | DOI | MR | Zbl

[96] N. A. Vavilov, M. Yu. Mitrofanov, “The intersection of two Bruhat cells”, Dokl. Ros. Akad. Nauk, 377:1 (2001), 7–10 | MR | Zbl

[97] N. A. Vavilov, I. M. Pevzner, “Triples of long root subgroups”, J. Math. Sci., 147:5 (2007), 7005–7020 | DOI | MR

[98] N. Vavilov, E. Plotkin, “Chevalley groups over commutative rings. I. Elementary calculations”, Acta Appl. Math., 45:1 (2006), 73–113 | DOI | MR

[99] N. A. Vavilov, A. A. Semenov, “Long root semisimple elements in Chevalley groups”, Dokl. Akad. Nauk, 338:6 (1994), 725–727 | MR | Zbl

[100] N. A. Vavilov, A. A. Semenov, “Bruhat decomposition for long root tori in Chevalley groups”, J. Math. Sci., 57 (1991), 3453–3458 | DOI | MR

[101] N. A. Vavilov, A. A. Semenov, “Long root tori in Chevalley groups”, St. Petersburg Math. J., 24:3 (2013), 387–430 | DOI | MR | Zbl

[102] N. A. Vavilov, S. S. Sinchuk, “Dennis-Vaserstein type decompositions”, J. Math. Sci., 171:3 (2010), 331–337 | DOI | MR | Zbl

[103] N. A. Vavilov, Z. Zuhong, “Commutators of elementary subgroups:curioser and curioser”, Transformation Groups, 28 (2023), 487–504 | DOI | MR | Zbl

[104] E. Voronetsky, “Injective stability for odd unitary $K_1$”, J. Group Theory, 23:5 (2020), 781–800 | DOI | MR | Zbl

[105] E. Voronetsky, “Centrality of $K_2$-functors revisited”, J. Pure Appl. Alg., 225:4 (2020) | DOI | MR