The Structure of Complex Lie Groups

ISBN: 9781138454279 出版年：2001 页码：229 Lee, Dong Hoon CRC Press

COMPLEX LIE GROUPS Almost Complex Structure Complex Lie Groups Examples of Complex Lie Groups Automorphism Groups and Semidirect Products Universal Complexification of Real Lie Groups REPRESENTATIVE FUNCTIONS OF LIE GROUPS Basic Definitions of Representations Representative Functions and Proper Automorphisms Analytic Representative Functions Universal Algebraic Hull Relative Algebras of Representative Functions Unipotent Hull EXTENSION OF REPRESENTATIONS Some Examples Decomposition of R(G) Extension Lemmas Extensions of Representations Application of Extension Theorem THE STRUCTURE OF COMPLEX LIE GROUPS Abelian Complex Analytic Groups Semisimple Complex Analytic Groups Reductive Complex Analytic Groups Maximal Compact Subgroups and Reductivity Representation Radical of Analytic Groups Faithfully Representable Groups Conjugacy of Reductive Subgroups Unipotent Hull of Faithfully Representable Groups ALGEBRAIC SUBGROUPS OF COMPLEX LIE GROUPS Algebraic Subgroups of Analytic Groups Extension of Representations and Representative Functions Algebraic Group Structure of Reductive Subgroups The Maximal Algebraic Subgroup Further Properties of Reductive Groups OBSERVABILITY IN COMPLEX ANALYTIC GROUPS Pro-Affine Algebraic Groups and Observability Affine Algebraic Groups and Observability Algebraic Hull of Observable Analytic Subgroups Extension of Analytic Representative Functions Structure of Observable Subgroups of Complex Lie Groups APPENDIX 1: Elementary Theory of Lie Algebras APPENDIX 2: Pro-Affine Algebraic Groups