By Helmut Strade

The challenge of classifying the finite dimensional easy 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 constrained easy Lie algebra is classical or of Cartan kind. This conjecture used to be proved for *p* > 7 by way of Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the overall case of now not inevitably limited Lie algebras and *p* > 7 used to be introduced in 1991 through Strade and Wilson and at last proved through Strade in 1998. the ultimate Block-Wilson-Strade-Premet class Theorem is a landmark results of smooth arithmetic and will be formulated as follows: *Every uncomplicated finite dimensional easy 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 publication concerning the category of the easy Lie algebras over algebraically closed fields of attribute > three. the 1st quantity includes the equipment, examples and a primary category end result. This moment quantity offers perception within the constitution of tori of Hamiltonian and Melikian algebras. according to sandwich aspect tools because of A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, an entire evidence for the type of absolute toral rank 2 basic 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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