LEADER 04404nam 22006733 450 001 9910968798403321 005 20221005084603.0 010 $a9781470463458 010 $a1470463458 035 $a(CKB)5590000000549572 035 $a(MiAaPQ)EBC30167830 035 $a(Au-PeEL)EBL30167830 035 $a(RPAM)22076502 035 $a(PPN)256596409 035 $a(OCoLC)1237771112 035 $a(EXLCZ)995590000000549572 100 $a20221005d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Irreducible Subgroups of Exceptional Algebraic Groups 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2020. 215 $a1 online resource (204 pages) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 1307 300 $a"November 2020, volume 268, number 1307 (fourth of 6 numbers)." 311 08$a9781470443375 311 08$a1470443376 320 $aIncludes bibliographical references. 327 $aStrategy for the proofs of theorems 5.1-9.1 -- Irreducible subgroups of G2 -- Irreducible subgroups of F4 -- Irreducible subgroups of G = E6 -- Irreducible subgroups of G = E7 -- Irreducible subgroups of G = E8 -- Corollaries -- Tables for theorem 1 -- Composition factors for G-irreducible subgroups -- Composition factors for the action of Levi subgroups. 330 $a"This monograph is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we complete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected subgroup X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vno. 1307. 606 $aLinear algebraic groups 606 $aRepresentations of groups 606 $aEmbeddings (Mathematics) 606 $aMaximal subgroups 606 $aGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theory for linear algebraic groups$2msc 606 $aGroup theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields$2msc 606 $aGroup theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups$2msc 615 0$aLinear algebraic groups. 615 0$aRepresentations of groups. 615 0$aEmbeddings (Mathematics) 615 0$aMaximal subgroups. 615 7$aGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theory for linear algebraic groups. 615 7$aGroup theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields. 615 7$aGroup theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups. 676 $a512.2 686 $a20G05$a20G15$a20G41$2msc 700 $aThomas$b Adam R$01802232 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910968798403321 996 $aThe Irreducible Subgroups of Exceptional Algebraic Groups$94347805 997 $aUNINA