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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On simple reducible depth-two Lie algebras with classical reductive null component


Author: Thomas B. Gregory
Journal: Proc. Amer. Math. Soc. 85 (1982), 318-322
MSC: Primary 17B20; Secondary 17B50
MathSciNet review: 656092
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Abstract: We classify the simple finite-dimensional reducible graded Lie algebras of the form $ {L_{ - 2}} \oplus {L_{ - 1}} \oplus {L_0} \oplus {L_1} \oplus \cdots \oplus {L_k}$ over an algebraically closed field of characteristic greater than 3, where $ {L_0}$ is reductive and classical such that no nonzero element of the center of $ {L_0}$ annihilates $ {L_{ - 2}}$ and where $ {L_{ - 1}}$ is the sum of two proper $ {L_0}$-submodules.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0656092-7
PII: S 0002-9939(1982)0656092-7
Article copyright: © Copyright 1982 American Mathematical Society