Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cartan subalgebras of simple Lie algebras

Author: Robert Lee Wilson
Journal: Trans. Amer. Math. Soc. 234 (1977), 435-446
MSC: Primary 17B20
MathSciNet review: 0480650
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Abstract: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic $ p > 7$. Let H be a Cartan subalgebra of L, let $ L = H + {\Sigma _{\gamma \in \Gamma }}{L_\gamma }$ be the Cartan decomposition of L with respect to H, and let $ \bar H$ be the restricted subalgebra of Der L generated by ad H. Let T denote the maximal torus of $ \bar H$ and I denote the nil radical of $ \bar H$. Then $ \bar H = T + I$. Consequently, each $ \gamma \in \Gamma $ is a linear function on H.

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Article copyright: © Copyright 1977 American Mathematical Society