The restricted simple Lie algebras are of classical or Cartan type

摘要

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).