Lie algebras and algebraic groups
The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included. TOC:Preface.- Results on topological spaces.-2. Rings and modules.- Integral extensions.- Factorial rings.- Field extensions.- Finitely generated algebras.- Gradings and filtrations.- Inductive limits.- Sheaves of functions.- Jordan decomposition and some basic results on groups.- Algebraic sets.- Prevarieties and varieties.- Projective varieties.- Dimension.- Morphisms and dimension.- Tangent spaces.- Normal varieties.- Root systems.- Lie algebras.- Semisimple and reductive Lie algebras.- Algebraic groups.- Affine algebraic groups.- Lie algebra of an algebraic group.- Correspondence between groups and Lie algebras.- Homogeneous spaces and quotients.- Solvable groups.- Reductive groups.- Borel subgroups, parabolic subgroups and Cartan subgroups.- Cartan subalgebras, Borel subalgebras and parabolic subalgebras.- Representations of semisimple Lie algebras.- Symmetric invariants.- S-triples.- Polarizations.- Results on orbits.- Centralizers.- S -root systems.- Symmetric Lie algebras.- Semisimple symmetric Lie algebras.- Sheets of Lie algebras.- Index and linear forms.- References.- Index of notations.- Index of terminologies
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783540241706
3540241701
- Maße
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24 cm
- Umfang
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XVI, 653 S.
- Sprache
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Englisch
- Anmerkungen
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Literaturverz. S. 641 - 644
- Klassifikation
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Mathematik
- Schlagwort
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Lie-Algebra
Algebraische Gruppe
- Ereignis
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Veröffentlichung
- (wo)
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Berlin, Heidelberg, New York
- (wer)
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Springer
- (wann)
-
2005
- Urheber
- Inhaltsverzeichnis
- Rechteinformation
-
Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Letzte Aktualisierung
-
11.06.2025, 13:42 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Tauvel, Patrice
- Yu, Rupert W. T.
- Springer
Entstanden
- 2005
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