Lie groups and Lie algebras, part I (chapters 1-3)

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Title To the reader Contents of the Elements of Mathematics series Contents I. Lie Algebras § 1. Definition of Lie algebras § 2. Enveloping algebra of a Lie algebra § 3. Representations § 4. Nilpotent Lie algebras § 5. Solvable Lie algebras § 6. Semi-simple Lie algebras § 7. Ado's theorem Exercises II. Free Lie Algebras § 1. Enveloping bigebra of a Lie algebra § 2. Free Lie algebras § 3. Enveloping algebra of the free Lie algebra § 4. Central filtrations § 5. Magnus algebras § 6. The Hausdorff series § 7. Convergence of the Hausdorff series (real or complex case) § 8. Convergence of the Hausdorff series (ultrametric case) Appendix: Möbius function Exercises III. Lie Groups § 1. Lie groups § 2. Group of tangent vectors to a Lie group § 3. Passage from a Lie group to its Lie algebra § 4. Passage from Lie algebras to Lie groups § 5. Formal calculations in Lie groups § 6. Real and complex Lie groups § 7. Lie groups over an ultrametric field § 8. Lie groups over R and Qp § 9. Commutators, centralizers and normalizers in a Lie group § 10. The automorphism group of a Lie group Appendix: Operations on linear representations Exercises Historical note Bibliography Index of notation Index of terminology Summary of certain properties of finite-dimensional Lie algebras over a field of characteristic 0