Geodesic
On the Extensions of Lie Algebras
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1439-1450

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give some results on the extensions of Lie algebras, with emphasis on the case of prime characteristic, although part of the paper is also of interest at characteristic 0. An extension of a Lie algebra L is a pair (E, π), where £ is a Lie algebra and π is a homomorphism of E onto L. The kernel K of the extension is ker π. 
Block, Richard E. On the Extensions of Lie Algebras. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1439-1450. doi: 10.4153/CJM-1968-145-5
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[1] 1. Albert, A. A. and Frank, M. S., Simple Lie algebras of characteristic p, Univ. e Politec. Torino Rend. Sem. Mat. 14 (1954-55), 117–139. Google Scholar

[2] 2. Barnes, R. T., On splitting fields for certain Lie algebras of prime characteristic, Proc. Amer. Math. Soc. 17 (1966), 930–935. Google Scholar

[3] 3. Block, R. E., On torsion-free abelian groups and Lie algebras, Proc. Amer. Math. Soc. 9 1958), 613–620. Google Scholar

[4] 4. Block, R. E., Trace forms on Lie algebras, Can. J. Math. 14 (1962), 553–564. Google Scholar

[5] 5. Block, R. E., The Lie algebras with a quotient trace form, Illinois J. Math. 9 (1965), 277–285. Google Scholar

[6] 6. Block, R. E., On the Mills-Seligman axioms for Lie algebras of classical type, Trans. Amer. Math. Soc. 121 (1966), 378–392. Google Scholar

[7] 7. Block, R. E. and Zassenhaus, H., The Lie algebras with a non-degenerate trace form, Illinois J. Math. 8 (1964), 543–549. Google Scholar

[8] 8. Campbell, H. E., On the Casimir operator, Pacific J. Math. 7 (1957), 1325–1331. Google Scholar

[9] 9. Chevalley, C., Théorie des groupes de Lie, Tome III, Théorèmes généraux sur les algèbres de Lie, Actualités Sci. Indust., No. 1226 (Hermann, Paris, 1955). Google Scholar

[10] 10. Curtis, C. W., Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307–326. Google Scholar

[11] 11. Curtis, C. W., On the dimensions of the irreducible modules of Lie algebras of classical type, Trans. Amer. Math. Soc. 96 (1960), 135–142. Google Scholar

[12] 12. Freudenthal, H., The existence of a vector of weight in irreducible Lie groups without centre, Proc. Amer. Math. Soc. 7 (1956), 175–176. Google Scholar

[13] 13. Jacobson, N., Lie algebras (Interscience, New York, 1962). Google Scholar

[14] 14. Mills, W. H. and Seligman, G. B., Lie algebras of classical type, J. Math. Mech. 6 (1957), 519–548. Google Scholar

[15] 15. Ree, R., On generalized Witt algebras, Trans. Amer. Math. Soc. 83 (1956), 510–546. Google Scholar

[16] 16. Steinberg, R., Générateurs, relations et revêtements des groupes algébriques, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962), pp. 113–127, Librairie Universitaire, Louvain (Gauthier-Villars, Paris, 1962). Google Scholar

[17] 17. Zassenhaus, H., Ueber Lie'sche Ringe mit Primzahlcharakteristik, Abh. Math. Sem. Univ. Hamburg 13 (1939), 1–100. Google Scholar

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