Titlebook: Complex Semisimple Lie Algebras; Jean-Pierre Serre Book 1987 Springer Science+Business Media New York 1987 algebra.lie algebra.lie group.r

Permanent

Folgen und Wirkungen des VerkehrsIn this chapter, g denotes a complex semisimple Lie algebra, h a Cartan subalgebra of g, and . the corresponding root system. We choose a base . = {..,...,..} of ., and we denote by .. the set of positive roots (with respect to .).

Innocence

Folgen und Wirkungen des VerkehrsThis chapter contains no proofs. All the Lie groups considered (except in Sec. 7) are . groups.

GULLY

Nilpotent Lie Algebras and Solvable Lie Algebras,The Lie algebras considered in this chapter are finite-dimensional algebras over a field .. In Secs. 7 and 8 we assume that . has characteristic O. The Lie bracket of . and y is denoted by [.], and the map y ? [.] by ad ..

endure

uveitis

Cartan Subalgebras,In this chapter (apart from Sec. 6) the ground field is the field . of complex numbers. The Lie algebras considered are finite dimensional.

流利圓滑

The Algebra sl2 and Its Representations,In this chapter (apart from Sec. 6) the ground field is the field C of complex numbers.

驚奇

Root Systems,In this chapter (apart from Sec. 17) the ground field is the field . of real numbers. The vector spaces considered are all finite dimensional.

乞討

cathartic

Linear Representations of Semisimple Lie Algebras,In this chapter, g denotes a complex semisimple Lie algebra, h a Cartan subalgebra of g, and . the corresponding root system. We choose a base . = {..,...,..} of ., and we denote by .. the set of positive roots (with respect to .).

Gratuitous