Publisher: Walter de Gruyter (April 26, 2004)
Format: PDF / Kindle / ePub
Size: 6.3 MB
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the matter of classifying the finite-dimensional uncomplicated Lie algebras over fields of attribute p > zero is a long-standing one. paintings in this query over the last 35 years has been directed by means of 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 variety. This conjecture was once 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 by way of Strade and Wilson and finally proved by way of Strade in 1998. the ultimate Block-Wilson-Strade-Premet type Theorem is a landmark results of sleek arithmetic and will be formulated as follows: each finite-dimensional basic Lie algebra over an algebraically closed box of attribute p > three is of classical, Cartan, or Melikian kind. within the three-volume publication, the writer is assembling the evidence of the category Theorem with reasons and references. The aim is a state of the art account at the constitution and type conception of Lie algebras over fields of optimistic attribute resulting in the leading edge of present examine during this box. this primary quantity is dedicated to getting ready the floor for the type paintings to be played within the moment quantity.