Lie algebras and algebraic groups

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Lie algebras and algebraic groups / Patrice Tauvel, Rupert W. T. Yu

資料種別:

図書

出版情報:

Berlin : Springer, c2005

形態:

xvi, 653 p. ; 25 cm

シリーズ名:

Springer monographs in mathematics <BA3386797X>

著者名:

ISBN:

9783540241706 [3540241701]

書誌ID:

BA71894751

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. [641]-644) and index

主題:

Lie algebras; Linear algebraic groups

言語:

英語

目次情報:

Preface

Results on topological spaces / 1：

Irreducible sets and spaces / 1.1：

Dimension / 1.2：

Noetherian spaces / 1.3：

Constructible sets / 1.4：

Gluing topological spaces / 1.5：

Rings and modules / 2：

Ideals / 2.1：

Prime and maximal ideals / 2.2：

Rings of fractions and localization / 2.3：

Localization of modules / 2.4：

Radical of an ideal / 2.5：

Local rings / 2.6：

Noetherian rings and modules / 2.7：

Derivations / 2.8：

Module of differentials / 2.9：

Integral extensions / 3：

Integral dependence / 3.1：

Integrally closed rings / 3.2：

Extensions of prime ideals / 3.3：

Factorial rings / 4：

Generalities / 4.1：

Unique factorization / 4.2：

Principal ideal domains and Euclidean domains / 4.3：

Polynomial and factorial rings / 4.4：

Symmetric polynomials / 4.5：

Resultant and discriminant / 4.6：

Field extensions / 5：

Extensions / 5.1：

Algebraic and transcendental elements / 5.2：

Algebraic extensions / 5.3：

Transcendence basis / 5.4：

Norm and trace / 5.5：

Theorem of the primitive element / 5.6：

Going Down Theorem / 5.7：

Fields and derivations / 5.8：

Conductor / 5.9：

Finitely generated algebras / 6：

Noether''s Normalization Theorem / 6.1：

Krull''s Principal Ideal Theorem / 6.3：

Maximal ideals / 6.4：

Zariski topology / 6.5：

Gradings and filtrations / 7：

Graded rings and graded modules / 7.1：

Graded submodules / 7.2：

Applications / 7.3：

Filtrations / 7.4：

Grading associated to a filtration / 7.5：

Inductive limits / 8：

Inductive systems of maps / 8.1：

Inductive systems of magmas, groups and rings / 8.3：

An example / 8.4：

Inductive systems of algebras / 8.5：

Sheaves of functions / 9：

Sheaves / 9.1：

Morphisms / 9.2：

Sheaf associated to a presheaf / 9.3：

Gluing / 9.4：

Ringed space / 9.5：

Jordan decomposition and some basic results on groups / 10：

Jordan decomposition / 10.1：

Generalities on groups / 10.2：

Commutators / 10.3：

Solvable groups / 10.4：

Nilpotent groups / 10.5：

Group actions / 10.6：

Generalities on representations / 10.7：

Examples / 10.8：

Algebraic sets / 11：

Affine algebraic sets / 11.1：

Regular functions / 11.2：

Examples of morphisms / 11.4：

Abstract algebraic sets / 11.6：

Principal open subsets / 11.7：

Products of algebraic sets / 11.8：

Prevarieties and varieties / 12：

Structure sheaf / 12.1：

Algebraic prevarieties / 12.2：

Morphisms of prevarieties / 12.3：

Products of prevarieties / 12.4：

Algebraic varieties / 12.5：

Rational functions / 12.6：

Local rings of a variety / 12.8：

Projective varieties / 13：

Projective spaces / 13.1：

Projective spaces and varieties / 13.2：

Cones and projective varieties / 13.3：

Complete varieties / 13.4：

Products / 13.5：

Grassmannian variety / 13.6：

Dimension of varieties / 14：

Dimension and the number of equations / 14.2：

System of parameters / 14.3：

Counterexamples / 14.4：

Morphisms and dimension / 15：

Criterion of affineness / 15.1：

Affine morphisms / 15.2：

Finite morphisms / 15.3：

Factorization and applications / 15.4：

Dimension of fibres of a morphism / 15.5：

Tangent spaces / 15.6：

A first approach / 16.1：

Zariski tangent space / 16.2：

Differential of a morphism / 16.3：

Some lemmas / 16.4：

Smooth points / 16.5：

Normal varieties / 17：

Normalization / 17.1：

Products of normal varieties / 17.3：

Properties of normal varieties / 17.4：

Root systems / 18：

Reflections / 18.1：

Root systems and bilinear forms / 18.2：

Passage to the field of real numbers / 18.4：

Relation between two roots / 18.5：

Base of a root system / 18.6：

Weyl chambers / 18.7：

Highest root / 18.8：

Closed subsets of roots / 18.9：

Weights / 18.10：

Graphs / 18.11：

Dynkin diagrams / 18.12：

Classification of root systems / 18.13：

Lie algebras / 19：

Generalities on Lie algebras / 19.1：

Representations / 19.2：

Nilpotent Lie algebras / 19.3：

Solvable Lie algebras / 19.4：

Radical and the largest nilpotent ideal / 19.5：

Nilpotent radical / 19.6：

Regular linear forms / 19.7：

Cartan subalgebras / 19.8：

Semisimple and reductive Lie algebras / 20：

Semisimple Lie algebras / 20.1：

Semisimplicity of representations / 20.2：

Semisimple and nilpotent elements / 20.4：

Reductive Lie algebras / 20.5：

Results on the structure of semisimple Lie algebras / 20.6：

Subalgebras of semisimple Lie algebras / 20.7：

Parabolic subalgebras / 20.8：

Algebraic groups / 21：

Subgroups and morphisms / 21.1：

Connectedness / 21.3：

Actions of an algebraic group / 21.4：

Modules / 21.5：

Group closure / 21.6：

Affine algebraic groups / 22：

Translations of functions / 22.1：

Jordan / 22.2：

Preface

Results on topological spaces / 1：

Irreducible sets and spaces / 1.1：

Dimension / 1.2：

Noetherian spaces / 1.3：

Constructible sets / 1.4：

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