Lie Groups, Lie AlgebrasPolished lecture notes provide a clean and usefully detailed account of the standard elements of the theory of Lie groups and algebras. Following nineteen pages of preparatory material, Part I (seven brief chapters) treats "Lie groups and their Lie algebras"; Part II (seven chapters) treats "complex semi-simple Lie algebras"; Part III (two chapters) treats "real semi-simple Lie algebras". The page design is intimidatingly dense, the exposition very much in the familiar "definition/lemma/proof/theorem/proof/remark" mode, and there are no exercises or bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR |
Contents
A Algebra | 1 |
B Functions of Operators | 9 |
E Topological Groups | 19 |
Local and Global Properties | 43 |
The Lie Algebra | 51 |
The Exponential Function | 62 |
Subgroups and Subalgebras | 73 |
Other editions - View all
Common terms and phrases
a₁ algebra of type basis C₁ Cartan subalgebra commutes complex Lie algebra conjugation connected Lie coordinate system Corollary curve defined dimension direct sum double neighbor Dynkin diagram easily verified eigenspace eigenvalues elements equation equivalent exists finite dimensional following lemma formula G₁ G₂ H₁ Hence Hermitian homomorphism ideal identity induction inner automorphism integer invariant irreducible representation isomorphic Lemma Lemma 9 Let G Lie group Lie subgroup linear functionals linear transformation M₁ manifold mapping matrix minimal weight multiplication natural bilinear form neighborhood nilpotent non-singular non-zero roots P₁ plainly preceding lemma proof of Lemma prove real Lie algebras root space section II.4 semi-simple set of roots signature simple Lie algebra simple set simply connected solvable subspace suppose T₁ tangent space tangent vector Theorem tion topology u₁ unique V₁ V₂ vector space w₁ Y₁