A new simple Lie algebra of characteristic three
Author:
Marguerite Frank
Journal:
Proc. Amer. Math. Soc. 38 (1973), 4346
MSC:
Primary 17B20
MathSciNet review:
0314924
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Abstract: We define a restricted simple algebra of dimension 18 over an arbitrary field of characteristic 3. From a certain property of its Cartan decomposition, we show to be nonisomorphic to any known algebra of identical dimension.
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 S. P. Demuškin, Cartan subalgebras of the simple Lie algebra and , Sibirsk. Mat. Ž. 11 (1970), 310325 = Siberian Math. J. 11 (1970), 233245. MR 41 #6919. MR 0262310 (41:6919)
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 N. Jacobson, Classes of restricted Lie algebras of characteristic . II, Duke Math. J. 10 (1943), 107121. MR 4, 187. MR 0007749 (4:187a)
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 I. Kaplansky, Lie algebras of characteristic , Trans. Amer. Math. Soc. 89 (1958), 149183. MR 20 #5799. MR 0099359 (20:5799)
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 A. I. Kostrikin, A parametric family of simple Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 744756 = Math. USSR Izv. 4 (1970), 751764. MR 43 #302. MR 0274539 (43:302)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197303149240
PII:
S 00029939(1973)03149240
Article copyright:
© Copyright 1973
American Mathematical Society
