LEADER 03792nam 2200553 450 001 9910807772903321 005 20230809223824.0 010 $a3-11-051689-6 010 $a3-11-051760-4 024 7 $a10.1515/9783110517606 035 $a(CKB)3710000001177228 035 $a(MiAaPQ)EBC4843238 035 $a(DE-B1597)473144 035 $a(OCoLC)984687181 035 $a(DE-B1597)9783110517606 035 $a(Au-PeEL)EBL4843238 035 $a(CaPaEBR)ebr11375537 035 $a(CaONFJC)MIL1006395 035 $a(OCoLC)983742311 035 $a(EXLCZ)993710000001177228 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$hVolume II$iClassifying the absolute toral rank two case /$fHelmut Strade 205 $aSecond edition. 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (386 pages) 225 1 $aDe Gruyter Expositions in Mathematics,$x0938-0572 ;$vVolume 42 311 $a3-11-051676-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tChapter 10. Tori in Hamiltonian and Melikian algebras -- $tChapter 11. 1-sections -- $tChapter 12. Sandwich elements and rigid tori -- $tChapter 13. Towards graded algebras -- $tChapter 14. The toral rank 2 case -- $tNotation -- $tBibliography -- $tIndex 330 $aThe problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p ? 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p ? 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p ? 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p ? 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p ? 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic ? 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic ? 3 is given. Contents Tori in Hamiltonian and Melikian algebras1-sectionsSandwich elements and rigid toriTowards graded algebrasThe toral rank 2 case 410 0$aDe Gruyter expositions in mathematics ;$vVolume 42. 606 $aLie algebras 610 $aLie algebras, fields of positive characteristic, classification. 615 0$aLie algebras. 676 $a512.55 700 $aStrade$b Helmut$052297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807772903321 996 $aSimple Lie algebras over fields of positive characteristic$91094029 997 $aUNINA