By Helmut Strade
The challenge of classifying the finite dimensional uncomplicated Lie algebras over fields of attribute p > zero is a long-standing 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 constrained uncomplicated Lie algebra is classical or of Cartan sort. This conjecture was once proved for p > 7 via Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the overall 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 by means of Strade in 1998. the ultimate Block-Wilson-Strade-Premet type Theorem is a landmark results of smooth 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.
In the three-volume e-book, the writer is assembling the evidence of the type Theorem with reasons and references. The target is a cutting-edge account at the constitution and category conception of Lie algebras over fields of optimistic attribute.
This first quantity is dedicated to getting ready the floor for the category paintings to be played within the moment and 3rd volumes. The concise presentation of the final conception underlying the subject material and the presentation of class effects on a subclass of the easy Lie algebras for all atypical primes will make this quantity a useful resource and reference for all learn mathematicians and complex graduate scholars in algebra. the second one version is corrected.
Toral subalgebras in p-envelopes
Lie algebras of unique derivations
Derivation basic algebras and modules
Simple Lie algebras
The isomorphism problem
Structure of straightforward Lie algebras
Pairings of precipitated modules
Toral rank 1 Lie algebras
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Structure Theory: Volume 1 (De Gruyter Expositions in Mathematics) by Helmut Strade