By Helmut Strade

The challenge of classifying the finite dimensional uncomplicated Lie algebras over fields of attribute *p* > zero is a protracted status one. paintings in this query has been directed through the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed box of attribute *p* > five a finite dimensional limited easy Lie algebra is classical or of Cartan sort. This conjecture was once proved for *p* > 7 through Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the final case of no longer inevitably limited Lie algebras and *p* > 7 used to be introduced in 1991 by way of Strade and Wilson and finally proved via Strade in 1998. the ultimate Block-Wilson-Strade-Premet class Theorem is a landmark results of sleek arithmetic and will be formulated as follows: *Every uncomplicated finite dimensional basic Lie algebra over an algebraically closed box of attribute p* > three *is of classical, Cartan, or Melikian type.*

This is the second one a part of a three-volume booklet concerning the class of the straightforward Lie algebras over algebraically closed fields of attribute > three. the 1st quantity includes the equipment, examples and a primary type outcome. This moment quantity offers perception within the constitution of tori of Hamiltonian and Melikian algebras. according to sandwich aspect tools as a result of A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, an entire facts for the type of absolute toral rank 2 easy Lie algebras over algebraically closed fields of attribute > three is given.

**Contents**

Tori in Hamiltonian and Melikian algebras

1-sections

Sandwich parts and inflexible tori

Towards graded algebras

The toral rank 2 case

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