Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2011_23_6_a0,
author = {N. A. Vavilov},
title = {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},
journal = {Algebra i analiz},
pages = {1--31},
publisher = {mathdoc},
volume = {23},
number = {6},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2011_23_6_a0/}
}
TY - JOUR AU - N. A. Vavilov TI - 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 JO - Algebra i analiz PY - 2011 SP - 1 EP - 31 VL - 23 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2011_23_6_a0/ LA - ru ID - AA_2011_23_6_a0 ER -
%0 Journal Article %A N. A. Vavilov %T 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 %J Algebra i analiz %D 2011 %P 1-31 %V 23 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/AA_2011_23_6_a0/ %G ru %F AA_2011_23_6_a0
N. A. Vavilov. 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. Algebra i analiz, Tome 23 (2011) no. 6, pp. 1-31. http://geodesic.mathdoc.fr/item/AA_2011_23_6_a0/
[1] Abe E., “Avtomorfizmy grupp Shevalle nad kommutativnymi koltsami”, Algebra i analiz, 5:2 (1993), 74–90 | MR | Zbl
[2] Borel A., “Svoistva i lineinye predstavleniya grupp Shevalle”, Seminar po algebraicheskim gruppam, Mir, M., 1973, 9–59 | MR
[3] Burbaki N., Gruppy i algebry Li, Gl. IV–VI, Mir, M., 1972 | MR
[4] Vavilov N. A., “Kak uvidet znaki strukturnykh konstant?”, Algebra i analiz, 19:4 (2007), 34–68 | MR
[5] Vavilov N. A., “Numerologiya kvadratnykh uravnenii”, Algebra i analiz, 20:5 (2008), 9–40 | MR
[6] Vavilov N. A., Gavrilovich M. R., “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya grupp Shevalle tipov $\mathrm E_6$ i $\mathrm E_7$”, Algebra i analiz, 16:4 (2004), 54–87 | MR | Zbl
[7] Vavilov N. A., Gavrilovich M. R., Nikolenko S. I., “Stroenie grupp Shevalle: dokazatelstvo iz Knigi”, Zap. nauch. semin. POMI, 330, 2006, 36–76 | MR | Zbl
[8] Vavilov N. A., Kazakevich V. G., “Esche odna variatsiya na temu razlozheniya transvektsii”, Vestn. S.-Peterburg. un-ta. Ser. 1, 2008, no. 4, 71–74 | Zbl
[9] Vavilov N. A., Kazakevich V. G., “Razlozhenie transvektsii dlya avtomorfizmov”, Zap. nauch. semin. POMI, 365, 2009, 47–62 | MR | Zbl
[10] Vavilov N. A., Kazakevich V. G., “Esche neskolko variatsii na temu razlozheniya transvektsii”, Zap. nauch. semin. POMI, 375, 2010, 32–47 | MR | Zbl
[11] Vavilov N. A., Luzgarev A. Yu., “Normalizator gruppy Shevalle tipa $\mathrm E_6$”, Algebra i analiz, 19:5 (2007), 37–64 | MR
[12] Vavilov N. A., Luzgarev A. Yu., “Normalizator gruppy Shevalle tipa $\mathrm E_7$” (to appear)
[13] Vavilov N. A., Luzgarev A. Yu., “Gruppa Shevalle tipa $\mathrm E_7$ v 56-mernom predstavlenii”, Zap. nauch. semin. POMI, 386, 2011, 5–99 | MR
[14] Vavilov N. A., Luzgarev A. Yu., “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya gruppy Shevalle tipa $\mathrm E_8$” (to appear)
[15] Vavilov N. A., Luzgarev A. Yu., Pevzner I. M., “Gruppa Shevalle tipa $\mathrm E_6$ v 27-mernom predstavlenii”, Zap. nauch. semin. POMI, 338, 2006, 5–68 | MR | Zbl
[16] Vavilov N. A., Nikolenko S. I., “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya grupp Shevalle tipa $\mathrm F_4$”, Algebra i analiz, 20:4 (2008), 27–63 | MR
[17] Vavilov N. A., Plotkin E. B., Stepanov A. V., “Vychisleniya v gruppakh Shevalle nad kommutativnymi koltsami”, Dokl. AN SSSR, 307:4 (1989), 788–791 | MR | Zbl
[18] Vavilov N. A., Stavrova A. K., “Osnovnye reduktsii v zadache opisaniya normalnykh podgrupp”, Zap. nauch. semin. POMI, 349, 2007, 30–52
[19] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Mat. sb., 30(72):2 (1952), 349–362 | MR | Zbl
[20] Luzgarev A. Yu., “O nadgruppakh $E(\mathrm E_6,R)$ i $E(\mathrm E_7,R)$ v minimalnykh predstavleniyakh”, Zap. nauch. semin. POMI, 319, 2004, 216–243 | MR | Zbl
[21] Luzgarev A. Yu., “Opisanie nadgrupp $\mathrm F_4$ v $\mathrm E_6$ nad kommutativnym koltsom”, Algebra i analiz, 20:6 (2008), 148–185 | MR
[22] Luzgarev A. Yu., Nadgruppy isklyuchitelnykh grupp, Kand. dis., SPbGU, SPb., 2008, 106 pp.
[23] Pevzner I. M., “Geometriya kornevykh elementov v gruppakh tipa $\mathrm E_6$”, Algebra i analiz, 23:3 (2011), 261–309 | MR
[24] Pevzner I. M., “Shirina grupp tipa $\mathrm E_6$ otnositelno mnozhestva kornevykh elementov. I”, Algebra i analiz, 23:5 (2011), 155–198 | MR
[25] Springer T. A., “Lineinye algebraicheskie gruppy”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 55, VINITI, M., 1989, 5–136 | MR | Zbl
[26] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl
[27] Tulenbaev M. S., “Multiplikator Shura gruppy elementarnykh matrits konechnogo poryadka”, Zap. nauch. semin. LOMI, 86, 1979, 162–169 | MR | Zbl
[28] Abe E., “Chevalley groups over local rings”, Tôhoku Math. J. (2), 21:3 (1969), 474–494 | DOI | MR | Zbl
[29] Abe E., “Chevalley groups over commutative rings”, Radical Theory (Sendai, 1988), Uchida Rokakuho, Tokyo, 1989, 1–23 | MR
[30] Abe E., “Normal subgroups of Chevalley groups over commutative rings”, Algebraic $\mathrm K$-Theory and Algebraic Number Theory (Honolulu, HI, 1987), Contemp. Math., 83, Amer. Math. Soc., Providence, RI, 1989, 1–17 | DOI | MR
[31] Abe E., Suzuki K., “On normal subgroups of Chevalley groups over commutative rings”, Tôhoku Math. J. (2), 28:2 (1976), 185–198 | DOI | MR | Zbl
[32] Carter R. W., “Conjugacy classes in the Weyl group”, Compositio Math., 25:1 (1972), 1–59 | MR | Zbl
[33] Carter R. W., Simple groups of Lie type, Pure Appl. Math., 28, Wiley, London et al., 1972 | MR
[34] van der Kallen W., “Another presentation for Steinberg groups”, Nederl. Akad. Wetensch. Proc. Ser. A, 80 (1977), 304–312 | MR | Zbl
[35] Matsumoto H., “Sur les sous-groupes arithmétiques des groupes semi-simples déployés”, Ann. Sci. École Norm. Sup. (4), 2 (1969), 1–62 | MR | Zbl
[36] Petrov V., Stavrova A., “Tits indices over semilocal rings”, Transform. Groups, 16:1 (2011), 193–217 | DOI | MR | Zbl
[37] Plotkin E., “On the stability of the $\mathrm K_1$-functor for Chevalley groups of type $\mathrm E_7$”, J. Algebra, 210 (1998), 67–85 | DOI | MR | Zbl
[38] Plotkin E., Semenov A., Vavilov N., “Visual basic representations: an atlas”, Internat. J. Algebra Comput., 8:1 (1998), 61–95 | DOI | MR | Zbl
[39] Stein M. R., “Generators, relations and coverings of Chevalley groups over commutative rings”, Amer. J. Math., 93:4 (1971), 965–1004 | DOI | MR | Zbl
[40] Stein M. R., “Stability theorems for $\mathrm K_1$, $\mathrm K_2$ and related functors modeled on Chevalley groups”, Japan. J. Math. (N.S.), 4:1 (1978), 77–108 | MR | Zbl
[41] Stepanov A., Vavilov N., “Decomposition of transvections: a theme with variations”, $\mathrm K$-Theory, 19 (2000), 109–153 | MR | Zbl
[42] Vavilov N., “Structure of Chevalley groups over commutative rings”, Nonassociative Algebras and Related Topics (Hiroshima, 1990), World Sci. Publ., River Edge, NJ, 1991, 219–335 | MR | Zbl
[43] Vavilov N., “A third look at weight diagrams”, Rend. Sem. Mat. Univ. Padova, 104 (2000), 201–250 | MR | Zbl
[44] Vavilov N. A., “Do it yourself structure constants for Lie algebras of type $\mathrm E_l$”, Zap. nauch. semin. POMI, 281, 2001, 60–104 | MR | Zbl
[45] Vavilov N., “An $\mathrm A_3$-proof of structure theorems for Chevalley groups of types $\mathrm E_6$ and $\mathrm E_7$”, Internat. J. Algebra Comput., 17:5–6 (2007), 1283–1298 | DOI | MR | Zbl
[46] Vavilov N. A., Luzgarev A. Yu, Stepanov A. V., “Calculations in exceptional groups over rings”, Zap. nauch. semin. POMI, 373, 2009, 48–72 | MR
[47] Vavilov N., Plotkin E., “Chevalley groups over commutative rings. I. Elementary calculations”, Acta Appl. Math., 45 (1996), 73–115 | DOI | MR