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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Renate Carlsson
Journal: Trans. Amer. Math. Soc. 244 (1978), 173-184
MSC: Primary 17A30; Secondary 17D10
MathSciNet review: 506614
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0506614-5
PII: S 0002-9947(1978)0506614-5
Keywords: Malcev algebras, Malcev modules, exceptional simple non-Lie Malcev algebras, exceptional complete reducibility, Wedderburn principal theorem, Lie algebras, Cayley algebras, Lie modules
Article copyright: © Copyright 1978 American Mathematical Society