Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (pages 211-213) and index.

1. Complex Lie Groups -- 1.1. Analytic Manifolds -- 1.2. Complex Lie Groups -- 1.3. Examples of Complex Lie Groups -- 1.4. The Automorphism Group -- 1.5. Universal Complexification -- 2. Representative Functions of Lie Groups -- 2.1. Basic Definitions -- 2.2. Algebras of Representative Functions -- 2.3. Proper Automorphism Groups -- 2.4. Analytic Representative Functions -- 2.5. Universal Algebraic Hull -- 2.6. Relative Algebras -- 2.7. Unipotent Hull -- 3. Extensions of Representations -- 3.1. Some Examples -- 3.2. Decomposition Theorem -- 3.3. Main Lemma -- 3.4. Extensions of Representations -- 3.5. Unipotent Analytic Groups -- 3.6. Application to Solvable Groups -- 4. The Structure of Complex Lie Groups -- 4.1. Abelian Complex Analytic Groups -- 4.2. Decomposition of the Adjoint Group -- 4.3. Semisimple Complex Analytic Groups -- 4.4. Reductive Complex Analytic Groups -- 4.5. Compact Subgroups of Reductive Groups -- 4.6. Representation Radical -- 4.7. Faithfully Representable Groups -- 4.8. Conjugacy of Reductive Subgroups -- 4.9. Unipotent Hull of Complex Lie Groups -- 5. Algebraic Subgroups in Lie Groups -- 5.1. Affine Algebraic Structure in Lie Groups -- 5.2. Extension Lemma -- 5.3. Affine Algebraic Structure on Reductive Groups -- 5.4. The Maximum Algebraic Subgroup -- 5.5. Further Properties of Reductive Groups -- 6. Observability in Complex Lie Groups -- 6.1. Pro-affine Groups and Observability -- 6.2. Observability in Algebraic Groups -- 6.3. Extension of Representative Functions -- 6.4. Structure of Observable Subgroups -- A. Elementary Theory of Lie Algebras -- B. Pro-affine Algebraic Groups.