Derivations and automorphisms of nonassociative matrix algebras

Benkart, G. M.; Osborn, J. M.

doi:10.1090/S0002-9947-1981-0594417-5

Derivations and automorphisms of nonassociative matrix algebras
HTML articles powered by AMS MathViewer

by G. M. Benkart and J. M. Osborn PDF

Trans. Amer. Math. Soc. 263 (1981), 411-430 Request permission

Abstract:

This paper studies the derivation algebra and the automorphism group of ${M_n}(A)$, $n \times n$ matrices over an arbitrary nonassociative algebra $A$ with multiplicative identity $1$. The investigation also includes results on derivations and automorphisms of the algebras obtained from ${M_n}(A)$ using the Lie product $[xy] = xy - yx$, and the Jordan product $x \circ y = \tfrac {1} {2}(xy + yx)$.

References

The algebra of color

14

I. N. Herstein, Topics in ring theory, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0271135
Nathan Jacobson, Abstract derivation and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), no. 2, 206–224. MR 1501922, DOI 10.1090/S0002-9947-1937-1501922-7
N. Jacobson, Structure of alternative and Jordan bimodules, Osaka Math. J. 6 (1954), 1–71. MR 64762
N. Jacobson, Exceptional Lie algebras, Lecture Notes in Pure and Applied Mathematics, vol. 1, Marcel Dekker, Inc., New York, 1971. MR 0284482
N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479–502. MR 38335, DOI 10.1090/S0002-9947-1950-0038335-X
Lawrence S. Levy, Artinian, non-Noetherian rings, J. Algebra 47 (1977), no. 2, 276–304. MR 447334, DOI 10.1016/0021-8693(77)90226-5
Wallace S. Martindale III, Lie derivations of primitive rings, Michigan Math. J. 11 (1964), 183–187. MR 166234
Wallace S. Martindale III, Lie isomorphisms of prime rings, Trans. Amer. Math. Soc. 142 (1969), 437–455. MR 251077, DOI 10.1090/S0002-9947-1969-0251077-5
Alex Rosenberg and Daniel Zelinsky, Automorphisms of separable algebras, Pacific J. Math. 11 (1961), 1109–1117. MR 148709

Algebraic groups