LEADER 04094nam 2200529 450 001 9910814026203321 005 20230809223803.0 010 $a3-11-051523-7 010 $a3-11-051544-X 024 7 $a10.1515/9783110515442 035 $a(CKB)3710000001177227 035 $a(MiAaPQ)EBC4843237 035 $a(DE-B1597)472781 035 $a(OCoLC)983735784 035 $a(OCoLC)986035677 035 $a(DE-B1597)9783110515442 035 $a(Au-PeEL)EBL4843237 035 $a(CaPaEBR)ebr11375536 035 $a(EXLCZ)993710000001177227 100 $a20170505h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aSimple lie algebras over fields of positive characteristic$hVolume I$iStructure theory /$fHelmut Strade 205 $aSecond edition. 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (542 pages) 225 1 $aDe Gruyter Expositions in Mathematics,$x0938-0572 ;$vVolume 38 311 $a3-11-051516-4 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tChapter 1. Toral subalgebras in p-envelopes -- $tChapter 2. Lie algebras of special derivations -- $tChapter 3. Derivation simple algebras and modules -- $tChapter 4. Simple Lie algebras -- $tChapter 5. Recognition theorems -- $tChapter 6. The isomorphism problem -- $tChapter 7. Structure of simple Lie algebras -- $tChapter 8. Pairings of induced modules -- $tChapter 9. Toral rank 1 Lie algebras -- $tNotation -- $tBibliography -- $tIndex 330 $aThe problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p ? 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p ? 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p ? 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p ? 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p ? 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras 410 0$aDe Gruyter expositions in mathematics ;$vVolume 38. 606 $aLie algebras 610 $aLie algebras, fields of positive characteristic, structure theory. 615 0$aLie algebras. 676 $a512.55 700 $aStrade$b Helmut$052297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814026203321 996 $aSimple Lie algebras over fields of positive characteristic$91094029 997 $aUNINA