Geodesic
Deformations of classical Lie algebras
Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1171-1190 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a classical Lie algebra $L$ of characteristic $p>2$ and different from $C_2$ it is proved that $H^2(L,L)=0$ when $p=3$. A classical Lie algebra is understood to be the Lie algebra of a simple algebraic group, or its quotient algebra by the centre, or a Lie algebra $A_l^z$ with $l+1\equiv 0(p)$ or $E_6^z$ when $p=3$. 
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M. I. Kuznetsov; N. G. Chebochko. Deformations of classical Lie algebras. Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1171-1190. http://geodesic.mathdoc.fr/item/SM_2000_191_8_a2/

[1] Rudakov A. N., “Deformatsii prostykh algebr Li”, Izv. AN SSSR. Ser. matem., 35 (1971), 1113–1119 | MR | Zbl

[2] Brown G., “Lie algebras of characteristic three with non-degenerate Killing form”, Trans. Amer. Math. Soc., 137 (1969), 259–268 | DOI | MR | Zbl

[3] Kostrikin A. I., “Parametricheskoe semeistvo prostykh algebr Li”, Izv. AN SSSR. Ser. matem., 34 (1970), 744–756 | MR | Zbl

[4] Dzhumadildaev A. S., “K deformatsiyam klassicheskikh prostykh algebr Li”, UMN, 31:3 (1976), 211–212 | MR | Zbl

[5] Kostrikin A. I., Kuznetsov M. I., “O deformatsiyakh klassicheskikh algebr Li kharakteristiki tri”, Dokl. RAN, 343:3 (1995), 299–301 | MR | Zbl

[6] Kirillov S. A., Kuznetsov M. I., Chebochko N. G., “O deformatsiyakh algebry Li tipa $G_2$ kharakteristiki tri”, Izv. vuzov. Matem. (to appear)

[7] Gerstenhaber M., “On the deforormation of rings and algebras”, Ann. of Math. (2), 79:1 (1964), 59–103 | DOI | MR | Zbl

[8] Frohardt D. E., Griess R. L.(Jr.)., “Automorphisms of modular Lie algebras”, Nova J. Algebra Geom., 1 (1992), 339–345 | MR | Zbl

[9] Springer T. A., Shteinberg R., “Klassy sopryazhennykh elementov”, Sb. trudov seminara po algebraicheskim gruppam, Mir, M., 1973, 162–262 | MR

[10] Seligman G. B., Modular Lie algebras, Springer-Verlag, New York, 1967 | MR | Zbl

[11] Burbaki N., Gruppy i algebry Li, Gl. IV–VI, Mir, M., 1972 | MR | Zbl

[12] Burbaki N., Gruppy i algebry Li, Gl. VII–VIII, Mir, M., 1978 | MR

[13] Kostrikin A. I., Ostrik V. V., “K teoreme raspoznavaniya dlya algebr Li kharakteristiki 3”, Matem. sb., 186:10 (1995), 73–88 | MR | Zbl

[14] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl