LEADER 03714nam 2200649 450 001 996466529903316 005 20220911152654.0 010 $a3-540-38864-8 024 7 $a10.1007/BFb0079295 035 $a(CKB)1000000000437505 035 $a(SSID)ssj0000322284 035 $a(PQKBManifestationID)12064918 035 $a(PQKBTitleCode)TC0000322284 035 $a(PQKBWorkID)10289923 035 $a(PQKB)10302986 035 $a(DE-He213)978-3-540-38864-7 035 $a(MiAaPQ)EBC5585751 035 $a(Au-PeEL)EBL5585751 035 $a(OCoLC)1066184792 035 $a(MiAaPQ)EBC6842169 035 $a(Au-PeEL)EBL6842169 035 $a(OCoLC)793079053 035 $a(PPN)155227033 035 $a(EXLCZ)991000000000437505 100 $a20220911d1988 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aConstructions of lie algebras and their modules /$fGeorge B. Seligman 205 $a1st ed. 1988. 210 1$aBerlin, Germany :$cSpringer-Verlag,$d[1988] 210 4$dİ1988 215 $a1 online resource (VIII, 196 p.) 225 1 $aLecture Notes in Mathematics ;$v1300 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-18973-4 311 $a3-540-18973-4 327 $aAn introductory example: sl(n,D) -- General considerations -- Involutorial algebras and modules for their skew elements -- Construction of modules with prescribed relative highest weights, for the isotropic algebras of chapter 3 -- Construction of exceptional algebras from quadratic forms -- Representations of exceptional algebras constructed from quadratic forms -- Non-reduced excepticnal algebras with a one-dimensional root space -- Construction of modules for the super-exceptional algebras of rank one -- Complements. 330 $aThis book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1300. 606 $aModules (Algebra) 606 $aLie algebras 606 $aTopological groups 615 0$aModules (Algebra) 615 0$aLie algebras. 615 0$aTopological groups. 676 $a512.74 700 $aSeligman$b George B.$f1927-$042120 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466529903316 996 $aConstructions of Lie algebras and their modules$978599 997 $aUNISA