LEADER 03805nam 2200577 450 001 9910827764803321 005 20180731044138.0 010 $a1-4704-0526-1 035 $a(CKB)3360000000465104 035 $a(EBL)3114217 035 $a(SSID)ssj0000889178 035 $a(PQKBManifestationID)11478251 035 $a(PQKBTitleCode)TC0000889178 035 $a(PQKBWorkID)10881945 035 $a(PQKB)11366345 035 $a(MiAaPQ)EBC3114217 035 $a(RPAM)15444583 035 $a(PPN)195418093 035 $a(EXLCZ)993360000000465104 100 $a20150417h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe recognition theorem for graded Lie algebras in prime characteristic /$fGeorgia Benkart, Thomas Gregory, Alexander Premet 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (164 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 197, Number 920 300 $a"Volume 197, Number 920 (second of 5 numbers)." 311 $a0-8218-4226-9 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Introduction""; ""Chapter 1. Graded Lie Algebras""; ""1.1. Introduction""; ""1.2. The Weisfeiler radical""; ""1.3. The minimal ideal J""; ""1.4. The graded algebras B(V[sub(-t)]) and B(V[sub(t)])""; ""1.5. The local subalgebra""; ""1.6. General properties of graded Lie algebras""; ""1.7. Restricted Lie algebras""; ""1.8. The main theorem on restrictedness (Theorem 1.63)""; ""1.9. Remarks on restrictedness""; ""1.10. The action of g[sub(0)] on g[sub(-j)]""; ""1.11. The depth-one case of Theorem 1.63""; ""1.12. Proof of Theorem 1.63 in the depth-one case"" 327 $a""2.7. Divided power algebras""""2.8. Witt Lie algebras of Cartan type (the W series)""; ""2.9. Special Lie algebras of Cartan type (the S series)""; ""2.10. Hamiltonian Lie algebras of Cartan type (the H series)""; ""2.11. Contact Lie algebras of Cartan type (the K series)""; ""2.12. The Recognition Theorem with stronger hypotheses""; ""2.13. g[sub(l)] as a g[sub(0)]-module for Lie algebras g of Cartan type""; ""2.14. Melikyan Lie algebras""; ""Chapter 3. The Contragredient Case""; ""3.1. Introduction""; ""3.2. Results on modules for three-dimensional Lie algebras"" 327 $a""3.3. Primitive vectors in g[sub(1)] and g[sub(-1)]""""3.4. Subalgebras with a balanced grading""; ""3.5. Algebras with an unbalanced grading""; ""Chapter 4. The Noncontragredient Case""; ""4.1. General assumptions and notation""; ""4.2. Brackets of weight vectors in opposite gradation spaces""; ""4.3. Determining g[sub(0)] and its representation on g[sub(-1)]""; ""4.4. Additional assumptions""; ""4.5. Computing weights of b[sup(a???)]-primitive vectors in g[sub(1)]""; ""4.6. Determination of the local Lie algebra""; ""4.7. The irreducibility of g[sub(1)]"" 327 $a""4.8. Determining the negative part when g[sub(1)] is irreducible""""4.9. Determining the negative part when g[sub(1)] is reducible""; ""4.10. The case that g[sub(0)] is abelian""; ""4.11. Completion of the proof of the Main Theorem""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 197, Number 920. 606 $aLie algebras 615 0$aLie algebras. 676 $a512/.482 700 $aBenkart$b Georgia$f1949-$060311 702 $aGregory$b Thomas Bradford$f1944- 702 $aPremet$b Alexander$f1955- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827764803321 996 $aThe recognition theorem for graded Lie algebras in prime characteristic$94112190 997 $aUNINA