02577nam 2200529 450 99646655940331620230420165415.0981-16-0475-4(CKB)4100000011807045(MiAaPQ)EBC6531631(Au-PeEL)EBL6531631(OCoLC)1244622358(PPN)254722881(EXLCZ)99410000001180704520211015d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAlgebra 4 lie algebras, Chevalley groups, and their representations /Ramji LalSingapore :Springer,[2021]©20211 online resource (332 pages)Infosys Science Foundation Series981-16-0474-6 Intro -- 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.Infosys Science Foundation series.Algebra fourAlgebraAlgebraTextbooksÀlgebrathubLlibres de textthubLlibres electrònicsthubAlgebra.AlgebraÀlgebraLlibres de text512.9Lal Ramji767330MiAaPQMiAaPQMiAaPQBOOK996466559403316Algebra 41894203UNISA