{"product_id":"structure-theory-9783110515169","title":"Structure Theory","description":"\u003cp\u003eThe problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p \u0026gt; 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p \u0026gt; 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p \u0026gt; 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p \u0026gt; 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: \u003cem\u003eEvery simple finite dimensional simple Lie algebra\u003c\/em\u003e \u003cem\u003eover an algebraically closed field of characteristic p \u0026gt; 3 is of classical, Cartan, or Melikian type.\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eIn the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThis first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eContents\u003c\/strong\u003e \u003c\/p\u003e \u003cp\u003eToral subalgebras in \u003cem\u003ep\u003c\/em\u003e-envelopes\u003cbr\u003eLie algebras of special derivations\u003cbr\u003eDerivation simple algebras and modules\u003cbr\u003eSimple Lie algebras\u003cbr\u003eRecognition theorems\u003cbr\u003eThe isomorphism problem\u003cbr\u003eStructure of simple Lie algebras\u003cbr\u003ePairings of induced modules\u003cbr\u003eToral rank 1 Lie algebras \u003c\/p\u003e","brand":"Helmut Strade","offers":[{"title":"Default Title","offer_id":48262153044219,"sku":"9783110515169","price":194.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0779\/3917\/9771\/files\/CoreSourceHub_a610d829-581f-4579-8558-ad2a33dbb3de.jpg?v=1778452382","url":"https:\/\/indiepubs.com\/products\/structure-theory-9783110515169","provider":"IndiePubs","version":"1.0","type":"link"}