By Helmut Strade
The challenge of classifying the finite dimensional easy Lie algebras over fields of attribute p > zero is an extended status one. paintings in this query has been directed via 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 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 final case of now not inevitably constrained Lie algebras and p > 7 was once introduced in 1991 by way of Strade and Wilson and finally proved by way of Strade in 1998. the ultimate Block-Wilson-Strade-Premet class Theorem is a landmark results of glossy arithmetic and will be formulated as follows: Every easy finite dimensional uncomplicated 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 in regards to the category of the easy Lie algebras over algebraically closed fields of attribute > three. the 1st quantity includes the tools, examples and a primary category outcome. This moment quantity provides perception within the constitution of tori of Hamiltonian and Melikian algebras. in accordance with sandwich aspect tools because of A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a whole facts for the class of absolute toral rank 2 basic Lie algebras over algebraically closed fields of attribute > three is given.
Tori in Hamiltonian and Melikian algebras
Sandwich parts and inflexible tori
Towards graded algebras
The toral rank 2 case
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The matter of classifying the finite dimensional basic Lie algebras over fields of attribute p > zero is a long-standing 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 uncomplicated Lie algebra is classical or of Cartan sort.
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Classifying the Absolute Toral Rank Two Case: Volume 2 (De Gruyter Expositions in Mathematics) by Helmut Strade