Titlebook: Algebra 4; Lie Algebras, Cheval Ramji Lal Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springe

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Representation Theory of Lie Algebras,Our main concern in this chapter will be to study and develop the representation theory and the character theory of semi-simple Lie algebras over an algebraically closed field of characteristic 0 including the theorem of Harish-Chandra and the Weyl, Kostant, and Steinberg formulas. We also establish the theorems of Ado and Iwasawa.

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Chevalley Groups,The purpose of this chapter is to introduce the classical groups as initial examples of Chevalley groups followed by the structure theory including the presentations of Chevalley groups. We also introduce and study the twisted groups of Lie types.

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Representation Theory of Chevalley Groups,This chapter is an introduction to the basic representation theory followed by the representation theory of Chevalley groups including the Steinberg representations, the principal series representations, the discrete series representations, and Deligne–Lusztig virtual characters.

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978-981-16-0477-5The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor

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