POD-李群与李代数III：李群和李代数的结构 (俄罗)奥尼契科科学出版社下载 mobi epub pdf 电子书 2024

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发表于2024-11-12

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出版社：科学出版社

ISBN：9787030235060

商品编码：27410705213

包装：精装

出版时间：2009-01-01

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图书基本信息
图书名称	POD-李群与李代数III：李群和李代数的结构	作者	(俄罗)奥尼契科
定价	118.00元	出版社	科学出版社
ISBN	9787030235060	出版日期	2009-01-01
字数		页码
版次	1	装帧	精装
开本	16开	商品重量	0.540Kg

内容简介

The book contains a prehensive account of the structure and classificatioof Lie groups and finite-dimensional Lie algebras(including semisimple， solvable， and of general type). Iparticular，a modem approach to the de*ioof automorphisms and gradings of semisimple Lie algebras is given. A special chapter is devoted to models ofthe exceptional Lie algebras. The book contains many tables and will serve as a reference. At the same time many results are acpanied by short proofs.Onishchik and Vinberg are internationally knowspecialists itheir field; they are also well knowfor their monograph 'Lie Groups and Algebraic Groups (Springer-Verlag 1990).The book will be immensely useful to graduate students idifferential geometry， algebra and theoretical physics.

作者简介

Introduction
Chapter 1．General Theorems
1．Lie's and Engel's Theorems
1．1．Lie's Theorem
1．2．Generalizations of Lie's Theorem
1．3．Engel's Theorem and Corollaries to It
1．4．AAnalogue of Engel's Theorem iGroup Theory
2．The CaftaCriterion
2．1．Invariant Bilinear Forms
2．2．Criteria of Solvability and Semisimplicity
2．3．Factorizatiointo Simple Factors
3．Complete Reducibility of Representations and Triviality of the Cohomology of Semisimple Lie Algebras
3．1．Cohomological Criterioof Complete Reducibility
3．2．The Casimir Operator
3．3．Theorems othe Triviality of Cohomology
3．4．Complete Reducibility of Representations
3．5．Reductive Lie Algebras
4．Levi Deposition
4．1．Levi's Theorem
4．2．Existence of a Lie Group with a GiveTangent Algebra
4．3．Malcev's Theorem
4．4．Classificatioof Lie Algebras with a GiveRadical
5．Linear Lie Groups
5．1．Basic Notions
5．2．Some Examples
5．3．Ado's Theorem
5．4．Criteria of Linearizability for Lie Groups．Linearizer
5．5．Sufficient Linearizability Conditions
5．6．Structure of Linear Lie Groups
6．Lie Groups and Algebraic Groups
6．1．Complex and Real Algebraic Groups
6．2．Algebraic Subgroups and Subalgebras
6．3．Semisimple and Reductive Algebraic Groups
6．4．Polar Deposition
6．5．Chevalley Deposition
7．Complexificatioand Real Forms
7．1．Complexificatioand Real Forms of Lie Algebras
7．2．Complexificatioand Real Forms of Lie Groups
7．3．Universal Complexificatioof a Lie Group
8．Splittings of Lie Groups and Lie Algebras
8．1．Malcev Splittable Lie Groups and Lie Algebras
8．2．Definitioof Splittings of Lie Groups and Lie Algebras
8．3．Theorem othe Existence and Uniqueness of Splittings
9．CaftaSubalgebras and Subgroups．Weights and Roots
9．1．Representations of Nilpotent Lie Algebras
9．2．Weights and Roots with Respect to a Nilpotent Subalgebra
9．3．CaftaSubalgebras
9．4．CaftaSubalgebras and Root Depositions of Semisimple Lie Algebras
9．5．CaftaSubgroups

Chapter 2．Solvable Lie Groups and Lie Algebras
1．Examples
2．Triangular Lie Groups and Lie Algebras
3．Topology of Solvable Lie Groups and Their Subgroups
3．1．Canonical Coordinates
3．2．Topology of Solvable Lie Groups
3．3．Aspherical Lie Groups
3．4．Topology of Subgroups of Solvable Lie Groups
4．Nilpotent Lie Groups and Lie Algebras
4．1．Definitions and Examples
4．2．Malcev Coordinates
4．3．Cohomology and Outer Automorphisms
5．Nilpotent Radicals iLie Algebras and Lie Groups
5．1．Nilradical
5．2．Nilpotent Radical
5．3．Unipotent Radical
6．Some Classes of Solvable Lie Groups and Lie Algebras
6．1．Characteristically Nilpotent Lie Algebras
6．2．Filiform Lie Algebras
6．3．Nilpotent Lie Algebras of Class 2
6．4．Exponential Lie Groups and Lie Algebras
6．5．Lie Algebras and Lie Groups of Type （I）
7．Linearizability Criteriofor Solvable Lie Groups

Chapter 3．Complex Semisimple Lie Groups and Lie Algebras
1．Root Systems
1．1．Abstract Root Systems
1．2．Root Systems of Reductive Groups
1．3．Root Depositions and Root Systems for Classical Complex Lie Algebras
1．4．Weyl Chambers and Simple Roots
1．5．Borel Subgroups and Subalgebras
1．6．The Weyl Group
1．7．The DynkiDiagram and the CartaMatrix
1．8．Classificatioof Admissible Systems of Vectors and Roo POD-李群与李代数III：李群和李代数的结构 (俄罗)奥尼契科科学出版社下载 mobi epub pdf txt 电子书格式