Abstract
The classical Lie algebras in the title are the Lie algebras of semisimple algebraic groups in prime characteristic. This includes the groups of exceptional type. The word classical was chosen to distinguish from the simple Lie algebras of Cartan type.
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References
H. H. Andersen: Extensions of modules for algebraic groups, Amer. J. Math. 106 (1984), 489–504
H. H. Andersen, J. C. Jantzen: Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1984), 487–525
N. Bourbaki: Groupes et algèbres de Lie, ch. IV, V et VI, Paris 1968 (Hermann)
Chiu Sen, Shen Guangyu: Cohomology of graded Lie algebras of Cartan type of characteristic p, Abh. Math. Sem. Univ. Hamburg 57 (1987), 139–156
E. Cline, B. Parshall, L. Scott: Cohomology, hyperalgebras, and representations, J. Algebra 63 (1980), 98–123
S. Donkin: On Ext1 for semisimple groups and infinitesimal subgroups, Math. Proc. Camb. Phil Soc. 92 (1982), 231–238
A. Džumadil’daev: On the cohomology of modular Lie algebras (russ.), Matem. Sbornik 119 (1982), 132–149 (engl. transi.: Math. USSR Sbornik 47 (1984), 127–143)
P. Gilkey, G. Seitz: Some representations of exceptional Lie algebras, Geometriae Dedicata 25 (1988), 407–416
G. Grélaud, C. Quitté, P. Tauvel: Bases de Chevalley et sl(2)-triplets des algèbres de Lie simples exceptionelles, preprint, Univ. de Poitiers, June 1990
G. Hochschild: Cohomology of restricted Lie algebras, Amer. J. Math. 76 (1954), 555–580
G. M. D. Hogeweij: Almost classical Lie algebras I, Indag. math. 44 (1982), 441–452
J. Humphreys: Introduction to Lie Algebras and Representation Theory, New York, etc., 1972 (Springer)
J. C. Jantzen: Darstellungen halbeinfacher algebraischer Gruppen und zugeordnete kontravariante Formen, Bonner math. Schriften 67(1973)
J. C. Jantzen: Weyl modules for groups of Lie type, pp.291–300 in: M. Collins (ed.), Finite Simple Groups II, Proc. Durham 1978, London etc. 1980 (Academic Press)
J. C. Jantzen: Representations of Algebraic Groups, Pure and Applied Mathematics, vol. 131, Boston, etc., 1987 (Academic)
W. van der Kallen: Infinitesimally central extensions of Chevalley groups, Lecture Notes in Mathematics 356, Berlin, etc.,1973(Springer)
Z. Lin: Extensions between simple modules for Frobenius kernels, to appear
A. A. Premet, I. D. Suprunenko: The Weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights, Commun. Algebra 11 (1983), 1309–1342
T. A. Springer: Weyl’s character formula for algebraic groups, Invent, math. 5 (1968), 85–105
J. B. Sullivan: Relations between the cohomology of an algebraic group and its infinitesimal subgroups, Amer. J. Math. 100 (1978), 995–1014
J. B. Sullivan: Lie algebra cohomology at irreducible modules, Ill. J. Math. 23(1979), 363–373
J. B. Sullivan: The second Lie algebra cohomology group and Weyl modules, Pacific J. Math. 86 (1980), 321–326
F. Veldkamp: Representations of algebraic groups of type F 4 in characteristic 2, J. Algebra 16 (1970), 326–339
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Jantzen, J.C. (1991). First Cohomology Groups for Classical Lie Algebras. In: Michler, G.O., Ringel, C.M. (eds) Representation Theory of Finite Groups and Finite-Dimensional Algebras. Progress in Mathematics, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8658-1_11
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DOI: https://doi.org/10.1007/978-3-0348-8658-1_11
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