Titlebook: Complex Semisimple Lie Algebras; Jean-Pierre Serre Book 2001 Springer-Verlag Berlin Heidelberg 2001 Lie algebra.Lie algebras.Matrix.Repres

BRAWL

TEN

,Anlagen für den ruhenden Kraftverkehr,In this chapter, . denotes a complex semisimple Lie algebra, . a Cartan subalgebra of . and . the corresponding root system. We choose a base . = α.,…, α. of ., and we denote by . the set of positive roots (with respect to .).

Horizon

https://doi.org/10.1007/978-3-662-25020-4This chapter contains no proofs. All the Lie groups considered (except in Sec. 7) are . groups.

公式

Nilpotent Lie Algebras and Solvable Lie Algebras,The Lie algebras considered in this chapter are finite-dimensional algebras over a field .. In Sees. 7 and 8 we assume that . has characteristic 0. The Lie bracket of . and . is denoted by [.], and the map . → [.] by ad ..

曲解

Semisimple Lie Algebras (General Theorems),In this chapter, the base field . is a field of characteristic zero.The Lie algebras and vector spaces considered have finite dimension over ..

Conflict

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.

CHASM

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

HILAR

直觉好

Structure of Semisimple Lie Algebras,Throughout this chapter, .denotes a ., and . a . of . (cf. Chap. III).

BAN

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