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  • ISBN:9787510070228
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 开本:24开
  • 页数:653
  • 出版时间:2014-03-01
  • 条形码:9787510070228 ; 978-7-5100-7022-8

本书特色

陶威尔编著的《李代数和代数群》内容介绍: the theory of groups and lie algebras is interesting for many reasons. in the mathematical viewpoint, it employs at the same time algebra, analysis and geometry. on the other hand, it intervenes in other areas of science, in particular in different branches of physics and chemistry. it is an active domain of current research. one of the difficulties that graduate students or mathematicians interested in the theory come across, is the fact that the theory has very much advanced,and consequently, they need to read a vast amount of books and articles before they could tackle interesting problems.

内容简介

本书属于Springer数学专著系列之一,秉承了这个系列的特点,经典,专业性强。本书分为40个小节,致力于李群和代数群理论的研究,包括大量的组合代数和代数几何知识,使得本书体系性更强。本书旨在将该理论的代数方面集中在一卷来讲述,展示了特征零中的理论基础。并且囊括了详细证明,在*后一节中讨论了一些*近结果。

目录

1 results on topological spaces
 1.1 irreducible sets and spaces
 1.2 dimension
 1.3 noetherian spaces
 1.4 constructible sets
 1.5 gluing topological spaces
2 rings and modules
 2.1 ideals
 2.2 prime and maximal ideals
 2.3 rings of fractions and localization
 2.4 localizations of modules
 2.5 radical of an ideal
 2.6 local rings
 2.7 noetherian rings and modules
 2.8 derivations
 2.9 module of differentials
3 integral extensions
 3.1 integral dependence
 3.2 integrally closed domains
 3.3 extensions of prime ideals
4 factorial rings
 4.1 generalities
 4.2 unique factorization
 4.3 principal ideal domains and euclidean domains
 4.4 polynomials and factorial rings
 4.5 symmetric polynomials
 4.6 resultant and discriminant
 field extensions
 5.1 extensions
 5.2 algebraic and transcendental elements
 5.3 algebraic extensions
 5.4 transcendence basis
 5.5 norm and trace
 5.6 theorem of the primitive element
 5.7 going down theorem
 5.8 fields and derivations
 5.9 conductor
 finitely generated algebras
 6.1 dimension
 6.2 noether's normalization theorem
 6.3 krull's principal ideal theorem
 6.4 maximal ideals
 6.5 zariski topology
7  gradings and filtrations
 7.1 graded rings and graded modules
 7.2 graded submodules
 7.3 applications
 7.4 filtrations
 7.5 grading associated to a filtration
 inductive limits
 8.1 generalities
 8.2 inductive systems of maps
 8.3 inductive systems of magmas, groups and rings
 8.4 an example
 8.5 inductive systems of algebras
 sheaves of functions
 9.1 sheaves
 9.2 morphisms
 9.3 sheaf associated to a presheaf
 9.4 gluing
  9.5 ringed space
10 jordan decomposition and some basic results on groups
  10.1 jordan decomposition
  10.2 generalities on groups
  10.3 commutators
  10.4 solvable groups
  10.5 nilpotent groups
 10.6 group actions
 10.7 generalities on representations
 10.8 examples
11 algebraic sets
 11.1 affine algebraic sets
 11.2 zariski topology
 11.3 regular functions
 11.4 morphisms
 11.5 examples of morphisms
 11.6 abstract algebraic sets
 11.7 principal open subsets
 11.8 products of algebraic sets
12 prevarieties and varieties
 12.1 structure sheaf
 12.2 algebraic prevarieties
 12.3 morphisms of prevarieties
 12.4 products of prevarieties
 12.5 algebraic varieties
 12.6 gluing
 12.7 rational functions
 12.8 local rings of a variety
13 projective varieties
 13.1 projective spaces
 13.2 projective spaces and varieties
 13.3 cones and projective varieties
 13.4 complete varieties
 13.5 products
 13.6 grassmannian variety
14 dimension
 14.1 dimension of varieties
 14.2 dimension and the number of equations .
 14.3 system of parameters
 14.4 counterexamples
15 morphisms and dimenion
 15.1 criterion of affineness
 15.2 afiine morphisms
 15.3 finite morphisms
 15.4 factorization and applications
 15.5 dimension of fibres of a morphism
 15.6 an example
16 tangent spaces
 16.1 a first approach
 16.2 zariski tangent space
 16.3 differential of a morphism
 16.4 some lemmas
 16.5 smooth points
17 normal varieties
 17.1 normal varieties
 17.2 normalization
 17.3 products of normal varieties
 17.4 properties of normal varieties
18 root systems
 18.1 reflections
 18.2 root systems
 18.3 root systems and bilinear forms
 18.4 passage to the field of real numbers
 18.5 relations between two roots
 18.6 examples of root systems
 18.7 base of a root system
 18.8 weyl chambers
 18.9 highest root
 18.10 closed subsets of roots
 18.11 weights
 18.12 graphs
 18.13 dynkin diagrams
 18.14 classification of root systems
19 lie algebras
 19.1 generalities on lie algebras
 19.2 representations
 19.3 nilpotent lie algebras
 19.4 solvable lie algebras
 19.5 radical and the largest nilpotent ideal
 19.6 nilpotent radical
 19.7 regular linear forms
 19.8 caftan subalgebras
20 semisimple and reductive lie algebras
 20.1 semisimple lie algebras
 20.2 examples
 20.3 semisimplicity of representations
 20.4 semisimple and nilpotent elements
 20.5 reductive lie algebras
 20.6 results on the structure of semisimple lie algebras
 20.7 subalgebras of semisimple lie algebras
 20.8 parabolic subalgebras
21 algebraic groups
 21.1 generalities
 21.2 subgroups and morphisms
 21.3 connectedness
 21.4 actions of an algebraic group
 21.5 modules
 21.6 group closure
22 ailine algebraic groups
 22.1 translations of functions
 22.2 jordan decomposition
 22.3 unipotent groups
 22.4 characters and weights
 22.5 tori and diagonalizable groups
 22.6 groups of dimension one
23 lie algebra of an algebraic group
 23.1 an associative algebra
 23.2 lie algebras
 23.3 examples
 23.4 computing differentials
 23.5 adjoint representation
 23.6 jordan decomposition
24 correspondence between groups and lie algebras
 24.1 notations
 24.2 an algebraic subgroup
 24.3 invariants
 24.4 functorial properties
 24.5 algebraic lie subalgebras
 24.6 a particular case
 24.7 examples
 24.8 algebraic adjoint group
25 homogeneous spaces and quotients
 25.1 homogeneous spaces
 25.2 some remarks
 25.3 geometric quotients
 25.4 quotient by a subgroup
 25.5 the case of finite groups
26 solvable groups
 26.1 conjugacy classes
 26.2 actions of diagonalizable groups
 26.3 fixed points
 26.4 properties of solvable groups
 26.5 structure of solvable groups
27 reductive groups
 27.1 radical and unipotent radical
 27.2 semisimple and reductive groups
 27.3 representations
 27.4 finiteness properties
 27.5 algebraic quotients
 27.6 characters
28 borel subgroups, parabolic subgroups, cartan subgroups
 28.1 borel subgroups
 28.2 theorems of density
 28.3 centralizers and tori
 28.4 properties of parabolic subgroups
 28.5 cartan subgroups
29 cartan subalgebras, borel subalgebras and parabolic
 subalgebras
 29.1 generalities
 29.2 cartan subalgebras
 29.3 applications to semisimple lie algebras
 29.4 borel subalgebras
 29.5 properties of parabolic subalgebras
 29.6 more on reductive lie algebras
 29.7 other applications
 29.8 maximal subalgebras
30 representations of semisimple lie algebras
  30.1 enveloping algebra
  30.2 weights and primitive elements
  30.3 finite-dimensional modules
  30.4 verma modules
  30.5 results on existence and uniqueness
  30.6 a property of the weyl group
31 symmetric invariants
  31.1 invariants of finite groups
  31.2 invariant polynomial functions
  31.3 a free module
32 s-triples
 32.1 jacobson-morosov theorem
 32.2 some lemmas
 32.3 conjugation of s-triples
 32.4 characteristic
 32.5 regular and principal elements
33 polarizations
 33.1 definition of polarizations
 33.2 polarizations in the semisimple case
 33.3 a non-polarizable element
 33.4 polarizable elements
 33.5 richardson's theorem
34 results on orbits
 34.1 notations
 34.2 some lemmas
 34.3 generalities on orbits
 34.4 minimal nilpotent orbit
 34.5 subregular nilpotent orbit
 34.6 dimension of nilpotent orbits
 34.7 prehomogeneous spaces of parabolic type
35 centralizers
 35.1 distinguished elements
 35.2 distinguished parabolic subalgebras
 35.3 double centralizers
 35.4 normalizers
 35.5 a semisimple lie subalgebra
 35.6 centralizers and regular elements
36 a-root systems
 36.1 definition
 36.2 restricted root systems
 36.3 restriction of a root
37 symmetric lie algebras
 37.1 primary subspaces
 37.2 definition of symmetric lie algebras
 37.3 natural subalgebras
 37.4 cartan subspaces
 37.5 the case of reductive lie algebras
 37.6 linear forms
38 semisimple symmetric lie algebras
 38.1 notations
 38.2 iwasawa decomposition
 38.3 coroots
 38.4 centralizers
 38.5 s-triples
 38.6 orbits
 38.7 symmetric invariants
 38.8 double centralizers
 38.9 normalizers
 38.10 distinguished elements
39 sheets of lie algebras
 39.1 jordan classes
 30.2 topology of jordan classes
 39.3 sheets
 39.4 dixmier sheets
 39.5 jordan classes in the symmetric case
 39.6 sheets in the symmetric case
40 index and linear forms
 40.1 stable linear forms
 40.2 index of a representation
 40.3 some useful inequalities
 40.4 index and semi-direct products
 40.5 heisenberg algebras in semisimple lie algebras
 40.6 index of lie subalgebras of borel subalgebras
 40.7 seaweed lie algebras
  40.8 an upper bound for the index/
  40.9 cases where the bound is exact
  40.10 on the index of parabolic subalgebras
references
list of notations
index
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作者简介

P.Tauvel是国际知名学者,在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果,适用于科研工作者、高校教师和研究生。

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