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The arithmetic theory of loop algebras. (English) Zbl 0383.17012


MSC:

17B65 Infinite-dimensional Lie (super)algebras
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References:

[1] Bourbaki, N., Groupes et algèbres de Lie (1968), Hermann: Hermann Paris, Chap. 4-6
[2] Garland, H.; Lepowsky, J., Lie algebra homology and the Macdonald-Kac formulas, Invent. Math., 34, 37-76 (1976) · Zbl 0358.17015
[3] Garland, H.; Raghunathan, M. S., A Bruhat decomposition for the loop space of a compact group: a new approach to results of Bott, (Proc. Nat. Acad. Sci. U.S.A., 72 (1975)), 4716-4717 · Zbl 0344.55009
[4] Jacobson, N., Lie Algebras (1962), Wiley: Wiley New York · JFM 61.1044.02
[5] Kac, V. G., Math. USSR-Izv., 2, 1271-1311 (1968), English translation · Zbl 0222.17007
[6] Kac, V. G., Functional Anal. Appl., 8, 68-70 (1974), English translation · Zbl 0299.17005
[7] Kostant, B., Groups over \(Z\), (Algebraic Groups and Discontinuous Subgroups. Algebraic Groups and Discontinuous Subgroups, Proceedings of Symposia in Pure Mathematics, Vol. 9 (1966), Amer. Math. Soc: Amer. Math. Soc Providence, R.I), 90-98
[8] Moody, R. V., A new class of Lie algebras, J. Algebra, 10, 211-230 (1968) · Zbl 0191.03005
[9] Moody, R. V., Euclidean Lie algebras, Canad. J. Math., 21, 1432-1454 (1969) · Zbl 0194.34402
[10] Serre, J.-P, Algèbres de Lie semi-simples complexes (1966), Benjamin: Benjamin New York · Zbl 0144.02105
[11] Steinberg, R., Lectures on Chevalley Groups, Yale University mimeographed notes (1967)
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