Cartan subalgebras of simple Lie algebras

Wilson, Robert Lee

doi:10.1090/S0002-9947-1977-0480650-9

Cartan subalgebras of simple Lie algebras
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by Robert Lee Wilson PDF

Trans. Amer. Math. Soc. 234 (1977), 435-446 Request permission

Correction: Trans. Amer. Math. Soc. 305 (1988), 851-855.

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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