Extraordinary book based on Moscow University hectographed notes from 1968. The book is substantially extended, with material developed through posing of problems and a wealth of examples. Several tables have never been published before, e.g. decomposition of representations into irreducible components. Especially interesting for physicists.
Reihe
Auflage
Softcover reprint of the original 1st ed. 1990
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 20 mm
Gewicht
ISBN-13
978-3-642-74336-8 (9783642743368)
DOI
10.1007/978-3-642-74334-4
Schweitzer Klassifikation
1. Lie Groups.- § 1. Background.- §2. Tangent Algebra.- §3. Connectedness and Simple Connectedness.- § 4. The Derived Algebra and the Radical.- 2. Algebraic Varieties.- §1. Affine Algebraic Varieties.- § 2. Projective and Quasiprojective Varieties.- § 3. Dimension and Analytic Properties of Algebraic Varieties.- 3. Algebraic Groups.- § 1. Background.- §2. Commutative and Solvable Algebraic Groups.- § 3. The Tangent Algebra.- §4. Compact Linear Groups.- 4. Complex Semisimple Lie Groups.- §1. Preliminaries.- §2. Root Systems.- §3. Existence and Uniqueness Theorems.- §4. Automorphisms.- 5. Real Semisimple Lie Groups.- § 1. Real Forms of Complex Semisimple Lie Groups and Algebras.- § 2. Compact Lie Groups and Reductive Algebraic Groups.- § 3. Cartan Decomposition.- § 4. Real Root Decomposition.- 6. Levi Decomposition.- 1°. Levi's Theorem.- 2°. Existence of a Lie Group with the Given Tangent Algebra.- 3°. Malcev's Theorem.- 4°. Algebraic Levi Decomposition.- Exercises.- Hints to Problems.- Reference Chapter.- § 1. Useful Formulae.- §2. Tables.
