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Transactions of the American Mathematical Society

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

 
 

 

Simple Lie algebras of toral rank one


Author: Robert Lee Wilson
Journal: Trans. Amer. Math. Soc. 236 (1978), 287-295
MSC: Primary 17B20
DOI: https://doi.org/10.1090/S0002-9947-1978-0463252-0
MathSciNet review: 0463252
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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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Article copyright: © Copyright 1978 American Mathematical Society