Simple Lie algebras of toral rank one

Wilson, Robert Lee

doi:10.1090/S0002-9947-1978-0463252-0

Simple Lie algebras of toral rank one
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Trans. Amer. Math. Soc. 236 (1978), 287-295 Request permission

Abstract:

Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic $p > 7$. Let L have Cartan decomposition $L = H + {\sum _{\gamma \in \Gamma }}{L_\gamma }$. If $\Gamma$ generates a cyclic group then L is isomorphic to ${\text {sl}}(2,F)$ or to one of the simple Lie algebras of generalized Cartan type $W(1:{\mathbf {n}})$ or $H{(2:{\mathbf {n}}:\Phi )^{(2)}}$.

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Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated

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