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Transactions of the American Mathematical Society
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
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0463252-0
PII: S 0002-9947(1978)0463252-0
Article copyright: © Copyright 1978 American Mathematical Society