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This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, Euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are more demanding.This text grew out of lectures which the author gave at the N.S.F. Advanced Science Seminar on Algebraic Groups at Bowdoin College in 1968.

Topological groups. Lie groups --- Lie algebras --- Representations of groups --- Representations of algebras --- Algèbres de Lie --- Représentations de groupes --- Représentations d'algèbres --- #TCPW W2.0 --- #TCPW W2.1 --- Algebra --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Lie algebras. --- Representations of groups. --- Representations of Lie algebras. --- Representations of Lie groups. --- Algèbres de Lie --- Représentations de groupes --- Représentations d'algèbres --- Representations of Lie algebras --- Lie, Algèbres de

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Group theory --- Groupes linéaires algébriques --- 512.74 --- Linear algebraic groups --- Algebraic groups, Linear --- Algebraic groups. Abelian varieties --- 512.74 Algebraic groups. Abelian varieties --- Groupes linéaires algébriques --- 512.54 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Geometry, Algebraic --- Algebraic varieties --- 512.54 Groups. Group theory --- Groups. Group theory --- Linear algebraic groups. --- Géométrie algébrique --- Groupes algébriques linéaires

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Conjugacy classes --- Lie algebras --- Linear algebraic groups --- Semisimple Lie groups --- 512.74 --- 512.74 Algebraic groups. Abelian varieties --- Algebraic groups. Abelian varieties --- Semi-simple Lie groups --- Lie groups --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Classes of conjugate elements

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Categories (Mathematics). --- Representations of Lie algebras.