LEADER 03736nam 22006614a 450 001 9910451460603321 005 20200520144314.0 010 $a1-282-19424-0 010 $a9786612194245 010 $a3-11-019794-4 024 7 $a10.1515/9783110197945 035 $a(CKB)1000000000520531 035 $a(EBL)314059 035 $a(OCoLC)435620160 035 $a(SSID)ssj0000246095 035 $a(PQKBManifestationID)11174069 035 $a(PQKBTitleCode)TC0000246095 035 $a(PQKBWorkID)10179858 035 $a(PQKB)10233528 035 $a(MiAaPQ)EBC314059 035 $a(DE-B1597)32307 035 $a(OCoLC)979581845 035 $a(DE-B1597)9783110197945 035 $a(PPN)140234721 035 $a(Au-PeEL)EBL314059 035 $a(CaPaEBR)ebr10194855 035 $a(CaONFJC)MIL219424 035 $a(OCoLC)935264246 035 $a(EXLCZ)991000000000520531 100 $a20040211g20049999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSimple Lie algebras over fields of positive characteristic$b[electronic resource] /$fby Helmut Strade 205 $aReprint 2014 210 $aNew York $cWalter de Gruyter$d2004- 215 $a1 online resource (548 p.) 225 1 $aDe Gruyter expositions in mathematics ;$v38 300 $aDescription based upon print version of record. 311 $a3-11-014211-2 320 $aIncludes bibliographical references (p. [527]-537) and index. 327 $a1. Structure theory 330 $aThe problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p ? 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p ? 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p ? 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p ? 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p ? 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volume. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra. 410 0$aGruyter expositions in mathematics ;$v38. 606 $aLie algebras 608 $aElectronic books. 615 0$aLie algebras. 676 $a512/.55 700 $aStrade$b Helmut$f1942-$052297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451460603321 996 $aSimple Lie algebras over fields of positive characteristic$91094029 997 $aUNINA