POD-李群與李代數III：李群和李代數的結構 (俄羅)奧尼契科科學齣版社 pdf epub mobi txt 電子書下載 2025

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俄羅奧尼契科著

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李群
李代數
數學
拓撲學
代數
幾何學
俄文
奧尼契科
科學齣版社
結構理論

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齣版社：科學齣版社

ISBN：9787030235060

商品編碼：27410705213

包裝：精裝

齣版時間：2009-01-01

具體描述

圖書基本信息
圖書名稱	POD-李群與李代數III：李群和李代數的結構	作者	(俄羅)奧尼契科
定價	118.00元	齣版社	科學齣版社
ISBN	9787030235060	齣版日期	2009-01-01
字數		頁碼
版次	1	裝幀	精裝
開本	16開	商品重量	0.540Kg

內容簡介

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.

作者簡介

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 Root Systems
1．9．Root and Weight Lattices
1．10．Chevalley Basis
2．Classificatioof Complex Semisimple Lie Groups and Their Linear Representations
2．1．Uniqueness Theorems for Lie Algebras
2．2．Uniqueness Theorem for Linear Representations
2．3．Existence Theorems
2．4．Global Structure of Connected Semisimple Lie Groups
2．5．Classificatioof Connected Semisimple Lie Groups
2．6．Linear Representations of Connected Reductive Algebraic Groups
2．7．Dual Representations and Bilinear Invariants
2．8．The Kernel and the Image of a Locally Faithful Linear Representation
2．9．The Casimir Operator and DynkiIndex
2．10．Spinor Group and Spinor Representation
3．Automorphisms and Gradings
3．1．Descriptioof the Group of Automorphisms
3．2．Quasitori of Automorphisms and Gradings
3．3．Homogeneous Semisimple and Nilpotent Elements
3．4．Fixed Points of Automorphisms
3．5．One—dimensional Tori of Automorphisms and Z—gradings
3．6．Canonical Form of aInner Semisimple Automorphism
3．7．Inner Automorphisms of Finite Order and Zm—gradings of Inner Type
3．8．Quasitorus Associated with a Component of the Group of Automorphisms
3．9．Generalized Root Deposition
3．10．Canonical Form of aOuter Semisimple Automorphism
3．11．Outer Automorphisms of Finite Order and Zm—gradings of Outer Type
3．12．JordaGradings of Classical Lie Algebras
3．13．JordaGradings of Exceptional Lie Algebras

Chapter 4．Real Semisimple Lie Groups and Lie Algebras
1．Classificatioof Real Semisimple Lie Algebras
1．1．Real Forms of Classical Lie Groups and Lie Algebras
1．2．Compact Real Form
1．3．Real Forms and Involutory Automorphisms
1．4．Involutory Automorphisms of Complex Simple Algebras
1．5．Classificatioof Real Simple Lie Algebras
2．Compact Lie Groups and Complex Reductive Groups
2．1．Some Properties of Linear Representations of Compact Lie Groups
2．2．Selfoadjointness of Reductive Algebraic Groups
2．3．Algebralcity of a Compact Lie Group
2．4．Some Properties of Extensions of Compact Lie Groups
2．5．Correspondence BetweeReal Compact and Complex Reductive Lie Groups
2．6．Maximal Tori iCompact Lie Groups
3．CartaDeposition
3．1．CartaDepositioof a Semisimple Lie Algebra
3．2．CaftaDepositioof a Semisimple Lie Group
3．3．Conjugacy of Maximal Compact Subgroups of Semisimple Lie Groups
3．4．Topological Structure of Lie Groups
3．5．Classificatioof Connected Semisimple Lie Groups
3．6．Linearizer of a Semisimple Lie Group
4．Real Root Deposition
4．1．Maximal R—Diagonalizable Subalgebras
4．2．Real Root Systems
4．3．Satake Diagrams
4．4．Split Real Semisimple Lie Algebras
4．5．Iwasawa Deposition
4．6．Maximal Connected Triangular Subgroups
4．7．CartaSubalgebras of a Real Semisimple Lie Algebra
5．Exponential Mapping for Semisimple Lie Groups
5．1．Image of the Exponential Mapping
5．2．Index of aElement of a Lie Group
5．3．Indices of Simple Lie Groups

Chapter 5．Models of Exceptional Lie Algebras
1．Models Associated with the Cayley Algebra
1．1， Cayley Algebra
1．2．The Algebra G2
1．3．Exceptional JordaAlgebra
1．4．The Algebra F4
1．5．The Algebra E6
1．6．The Algebra E7
1．7．Unified Constructioof Exceptional Lie Algebras
2．Models Associated with Gradings

Chapter 6．Subgroups and Subalgebras of Semisimple Lie Groups and Lie Algebras
1．Regular Subalgebras and Subgroups
1．1．Regular Subalgebras of Complex Semisimple Lie Algebras
1．2．Descriptioof Semisimple and Reductive Regular Subalgebras
1．3．Parabolic Subalgebras and Subgroups
1．4．Examples of Parabolic Subgroups and Flag Manifolds
1．5．Parabolic Subalgebras of Real Semisimple Lie Algebras
1．6．Nonsemisimple Maximal Subalgebras
2．Three—dimensional Simple Subalgebras and Nilpotent Elements
2．1．sι2—triples
2．2．Three—dimensional Simple Subalgebras of Classical Simple Lie Algebras
2．3．Principal and Semiprincipal Three—dimensional Simple Subalgebras
2．4．Minimal Ambient Regular Subalgebras
2．5．Minimal Ambient Complete Regular Subalgebras
3．Semisimple Subalgebras and Subgroups
3．1．Semisimple Subgroups of Complex Classical Groups
3．2．Maximal Connected Subgroups of Complex Classical Groups
3．3．Semisimple Subalgebras of Exceptional Complex Lie Algebras
3．4．Semisimple Subalgebras of Real Semisimple Lie Algebras

Chapter 7．Othe Classificatioof Arbitrary Lie Groups and Lie Algebras of a GiveDimension
1．Classificatioof Lie Groups and Lie Algebras of Small Dimension
1．1．Lie Algebras of Small1 Dimension
1．2．Connected Lie Groups of Dimensio< 3
2．The Space of Lie Algebras．Deformations and Contractions
2．1．The Space of Lie Algebras
2．2．Orbits of the Actioof the Group Gιn（k） oι（k）
2．3．Deformations of Lie Algebras
2．4．Rigid Lie Algebras
2．5．Contractions of Lie Algebras
2．6．Spaces ιn（k） for Small n
Tables
References
Author Index
Subject Index

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