On the exceptional central simple non-Lie Mal’cev algebras

Carlsson, Renate

doi:10.1090/S0002-9947-1978-0506614-5

On the exceptional central simple non-Lie Mal’cev algebras
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by Renate Carlsson

Trans. Amer. Math. Soc. 244 (1978), 173-184

DOI: https://doi.org/10.1090/S0002-9947-1978-0506614-5

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Abstract:

Malcev algebras belong to the class of binary Lie algebras. Any Lie algebra is a Malcev algebra. In this paper we show that for each seven-dimensional central simple non-Lie Malcev algebra any finite dimensional Malcev module is completely reducible also for positive characteristics. This contrasts with each modular semisimple Lie algebra. As a consequence we get that the classical structure theory for characteristic zero is valid also in the modular case if semisimplicity is replaced by ${G_1}$-separability. The Wedderburn principal theorem is proved for Malcev algebras.

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