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Irreducible representations of Lie \(p\)-algebras. (English. Russian original) Zbl 0237.17003

Funct. Anal. Appl. 5, 111-117 (1971); translation from Funkts. Anal. Prilozh. 5, No. 2, 28-36 (1971).

MSC:

17B50 Modular Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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References:

[1] B. Yu. Veisfeiler, ”Remarks on some algebraic groups,” Funktsional. Analiz i Ego Prilozhen.,4, No. 1, 91 (1970). · Zbl 0239.14012
[2] I. M. Gel’fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Theory of Representations and Automorphic Functions [in Russian], Nauka, Moscow (1966).
[3] N. Jacobson, Lie Algebras, Interscience, New York (1962).
[4] V. G. Kats, ”Simple irreducible graded Lie algebras of finite growth,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, 1323-1367 (1968).
[5] V. G. Kats, ”On a classification of simple Lie algebras over a field of nonzero characteristic,” Izv. Akad. Nauk SSSR., Ser. Matem.,34, 385-409 (1970).
[6] A. I. Kostrikin and I. R. Shafarevich, ”Graded Lie algebras of finite characteristic,” Izv. Akad. Nauk SSSR, Ser. Matem.,33, 251-322 (1969).
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[8] A. N. Rudakov and I. R. Shafarevich, ”Irreducible representations of a simple three-dimensional Lie algebra over a field of finite characteristic,” Matem. Zametki,2, No. 5, 439-454 (1967). · Zbl 0184.06002
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[10] A. Borel and T. A. Springer, ”Rationality properties of linear algebraic groups. II,” Tohoku Math. J.,20, No. 4, 443-497 (1968). · Zbl 0211.53302
[11] Ho-Jui Chang, Über Wittsche Lie-Ringe,” Abh. Math. Sem. Univ. Hamburg,14, 151-184 (1941). · Zbl 0025.24202
[12] C. W. Curtiss, ”Representations of Lie algebras of classical type with applications to linear groups,” J. Math. Mech.,9, 307-326 (1960). · Zbl 0089.25302
[13] Harish-Chandra, Automorphic Forms on Semi-simple Lie Groups, Lecture Notes in Mathematics, No. 62, Springer-Verlag, Berlin (1968). · Zbl 0186.04702
[14] H. Zassenhaus, ”Über Liesche Ringe mit Primzahlcharacteristik,” Abh. Math. Sem. Univ. Hamburg,13, No. 1/2, 1-100 (1939). · JFM 65.0090.01
[15] H. Zassenhaus, ”The representations of Lie algebras of prime characteristic,” Proc. Glasgow Math. Assoc.,2, No. 1, 1-36 (1954). · Zbl 0059.03001
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