On derivation algebras of Malcev algebras
Author:
Ernest L. Stitzinger
Journal:
Proc. Amer. Math. Soc. 62 (1977), 31-33
MSC:
Primary 17E05
DOI:
https://doi.org/10.1090/S0002-9939-1977-0424891-0
MathSciNet review:
0424891
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Abstract: It is shown that if A is a Malcev algebra over a field of characteristic 0, then A is semisimple if and only if the derivation algebra $\mathfrak {D}(A)$ is semisimple. It is then shown that A is semisimple if and only if ${A^\ast } = \mathfrak {L}(A) + \mathfrak {D}(A)$ is semisimple, where $\mathfrak {L}(A)$ is the Lie multiplication algebra of A.
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N. Bourbaki, Éléments de mathématique, Livre XXVI, Groupes et algèbres de Lie, Chap. I, Actualités Sci. Indust., no. 1285, Hermann, Paris, 1960. MR 24 #A2641.
- William H. Davenport, On inner derivations of Malcev algebras, Rocky Mountain J. Math. 2 (1972), no. 4, 565–568. MR 310026, DOI https://doi.org/10.1216/RMJ-1972-2-4-565
- E. N. Kuz′min, Mal′cev algebras and their representations, Algebra i Logika 7 (1968), no. 4, 48–69 (Russian). MR 0252468
- G. Leger and S. Tôgô, Characteristically nilpotent Lie algebras, Duke Math. J. 26 (1959), 623–628. MR 114841
- Ottmar Loos, Über eine Beziehung zwischen Malcev-Algebren und Lietripelsystemen, Pacific J. Math. 18 (1966), 553–562 (German, with English summary). MR 199236
- T. S. Ravisankar, Characteristically nilpotent algebras, Canadian J. Math. 23 (1971), 222–235. MR 276284, DOI https://doi.org/10.4153/CJM-1971-022-2
- T. S. Ravisankar, On Malcev algebras, Pacific J. Math. 42 (1972), 227–234. MR 313350
- Arthur A. Sagle, Malcev algebras, Trans. Amer. Math. Soc. 101 (1961), 426–458. MR 143791, DOI https://doi.org/10.1090/S0002-9947-1961-0143791-X
- Arthur A. Sagle, Simple Malcev algebras over fields of characteristic zero, Pacific J. Math. 12 (1962), 1057–1078. MR 150181
- Ernest L. Stitzinger, Malcev algebras with $J_{2}$-potent radical, Proc. Amer. Math. Soc. 50 (1975), 1–9. MR 374224, DOI https://doi.org/10.1090/S0002-9939-1975-0374224-1
- Ernest L. Stitzinger, On derivation algebras of Malcev algebras and Lie triple systems, Proc. Amer. Math. Soc. 55 (1976), no. 1, 9–13. MR 396713, DOI https://doi.org/10.1090/S0002-9939-1976-0396713-7
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Article copyright:
© Copyright 1977
American Mathematical Society
