The restricted simple Lie algebras are of classical or Cartan type.
The classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field F of prime characteristic p > 7 is announced. Such an algebra is either of classical type (an analogue over F of a finite-dimensional simple Lie algebra over the complex numbers) or of Cartan type (an analogue over F of one of the infinite Lie algebras of Cartan over the complex numbers).
Department of Mathematics, University of California, Riverside, CA 92521.
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Wilson