On derivation algebras of Malcev algebras and Lie triple systems

Stitzinger, Ernest L.

doi:10.1090/S0002-9939-1976-0396713-7

On derivation algebras of Malcev algebras and Lie triple systems
HTML articles powered by AMS MathViewer

by Ernest L. Stitzinger PDF

Proc. Amer. Math. Soc. 55 (1976), 9-13 Request permission

Abstract:

W. H. Davenport has shown that the derivation algebra $\mathfrak {D}(A)$ of a semisimple Malcev algebra $A$ of characteristic $0$ acts completely reducibly on $A$. The purpose of the present note is to characterize those Malcev algebras which have such derivation algebras as those whose radical is central and to obtain the same result for Lie triple systems. Analogous results are known to hold for standard and alternative algebras.

References

William H. Davenport, On inner derivations of Malcev algebras, Rocky Mountain J. Math. 2 (1972), no. 4, 565–568. MR 310026, DOI 10.1216/RMJ-1972-2-4-565

Mal’ cev algebras and their representations

7

40

William G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math. Soc. 72 (1952), 217–242. MR 45702, DOI 10.1090/S0002-9947-1952-0045702-9
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, On certain classes of Malcev algebras, J. Sci. Hiroshima Univ. Ser. A-I Math. 32 (1968), 233–236. MR 240156
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 10.1090/S0002-9947-1961-0143791-X
Richard D. Schafer, An introduction to nonassociative algebras, Pure and Applied Mathematics, Vol. 22, Academic Press, New York-London, 1966. MR 0210757
Ernest L. Stitzinger, Standard and alternative algebras with completely reducible derivation algebras, Proc. Amer. Math. Soc. 43 (1974), 57–62. MR 332914, DOI 10.1090/S0002-9939-1974-0332914-X
Ernest L. Stitzinger, Malcev algebras with $J_{2}$-potent radical, Proc. Amer. Math. Soc. 50 (1975), 1–9. MR 374224, DOI 10.1090/S0002-9939-1975-0374224-1

Additional Information

Journal: Proc. Amer. Math. Soc. 55 (1976), 9-13
DOI: https://doi.org/10.1090/S0002-9939-1976-0396713-7
MathSciNet review: 0396713