zbMATH — the first resource for mathematics

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).

17B50 Modular Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
Full Text: DOI
[1] B. Yu. Veisfeiler, ”Remarks on some algebraic groups,” Funktsional. Analiz i Ego Prilozhen.,4, No. 1, 91 (1970). · Zbl 0239.14012 · doi:10.1007/BF01094483
[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).
[7] A. N. Rudakov, ”On the representation of the classical Lie algebras in characteristic p,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, 735-743 (1970).
[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
[9] R. Block, ”The Lie algebras with a quotient trace form,” Canad. J. Math.,9, No. 2, 277-285 (1965). · Zbl 0135.07302
[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 · doi:10.2748/tmj/1178243073
[11] Ho-Jui Chang, Über Wittsche Lie-Ringe,” Abh. Math. Sem. Univ. Hamburg,14, 151-184 (1941). · Zbl 0025.24202 · doi:10.1007/BF02940743
[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 · doi:10.1007/BF02940753
[15] H. Zassenhaus, ”The representations of Lie algebras of prime characteristic,” Proc. Glasgow Math. Assoc.,2, No. 1, 1-36 (1954). · Zbl 0059.03001 · doi:10.1017/S2040618500032974
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.