Differential Geometry, Lie Groups, and Symmetric Spaces

2001/06/12 by Sigurđur Helgason · 18 citations
Mathematics · #Advanced Algebra and Geometry #Mathematics #Triple system #Pure mathematics #Symmetric space #Simple Lie group #Real form #Lie theory #Killing form #Representation of a Lie group #Lie group #Algebra over a field #Adjoint representation of a Lie algebra #Affine Lie algebra #Lie conformal algebra #Current algebra

paper · doi:10.1090/gsm/034

openalex publication_date 2001/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces Structure of semisimple Lie groups The classification of simple Lie algebras and of symmetric spaces Solutions to exercises Some details Bibliography List of notational conventions Symbols frequently used Index Reviews for the first edition.

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