LEADER 02577nam 2200529 450 001 996466559403316 005 20230420165415.0 010 $a981-16-0475-4 035 $a(CKB)4100000011807045 035 $a(MiAaPQ)EBC6531631 035 $a(Au-PeEL)EBL6531631 035 $a(OCoLC)1244622358 035 $a(PPN)254722881 035 $a(EXLCZ)994100000011807045 100 $a20211015d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebra 4 $elie algebras, Chevalley groups, and their representations /$fRamji Lal 210 1$aSingapore :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (332 pages) 225 1 $aInfosys Science Foundation Series 311 $a981-16-0474-6 327 $aIntro -- Preface -- Contents -- About the Author -- Notations -- 1 Lie Algebras -- 1.1 Definitions and Examples -- 1.2 Universal Enveloping Algebras: PBW Theorem -- 1.3 Solvable and Nilpotent Lie Algebras -- 1.4 Semi-Simple Lie Algebras -- 1.5 Extensions of Lie Algebras and Co-homology -- 2 Semi-Simple Lie Algebras and Root Systems -- 2.1 Root Space Decomposition -- 2.2 Root Systems -- 2.3 Dynkin Diagram and the Classification of Root Systems -- 2.4 Conjugacy Theorem, Existence and Uniqueness Theorems -- 3 Representation Theory of Lie Algebras -- 3.1 Theorems of Ado and Iwasawa -- 3.2 Cyclic Modules and Weights -- 3.3 Characters and Harish-Chandra's Theorem -- 3.4 Multiplicity Formulas of Weyl, Kostant, and Steinberg -- 4 Chevalley Groups -- 4.1 Classical Linear Groups -- 4.2 Chevalley Basis -- 4.3 Chevalley Groups -- 4.4 Twisted Groups -- 5 Representation Theory of Chevalley Groups -- 5.1 Language of Representation Theory -- 5.2 Representations of Sn, and of GL(2.q) -- 5.3 Steinberg Characters -- 5.4 Principal and Discrete Series Representations -- 5.5 Deligne-Lusztig Generalized Characters -- Appendix Bibliography -- -- Index. 410 0$aInfosys Science Foundation series. 517 3 $aAlgebra four 606 $aAlgebra 606 $aAlgebra$vTextbooks 606 $aÀlgebra$2thub 606 $aLlibres de text$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra. 615 0$aAlgebra 615 7$aÀlgebra 615 7$aLlibres de text 676 $a512.9 700 $aLal$b Ramji$0767330 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466559403316 996 $aAlgebra 4$91894203 997 $aUNISA