The matter of classifying the finite-dimensional easy Lie algebras over fields of attribute p > zero is a long-standing one. paintings in this query over the last forty five years has been directed by way of the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed box of attribute p > five a finite-dimensional constrained basic Lie algebra is classical or of Cartan variety. This conjecture was once proved for p > 7 through Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the overall case of no longer unavoidably constrained Lie algebras and p > 7 was once introduced in 1991 through Strade and Wilson and finally proved via Strade in 1998. the ultimate Block-Wilson-Strade-Premet type Theorem is a landmark results of glossy arithmetic and will be formulated as follows: each finite-dimensional uncomplicated Lie algebra over an algebraically closed box of attribute p > three is of classical, Cartan, or Melikian kind. within the three-volume booklet, the writer is assembling the facts of the category Theorem with causes and references. The aim is a state of the art account at the constitution and category conception of Lie algebras over fields of optimistic attribute resulting in the vanguard of present learn during this box. this is often the final of 3 volumes. during this monograph the facts of the class Theorem provided within the first quantity is concluded. It collects all of the very important effects at the subject which might be discovered merely in scattered clinical literatur thus far.
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