Author | Onishchik, Arkadij L. author |
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Title | Lie Groups and Algebraic Groups [electronic resource] / by Arkadij L. Onishchik, Ernest B. Vinberg |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1990 |
Connect to | http://dx.doi.org/10.1007/978-3-642-74334-4 |
Descript | XX, 330 p. online resource |
1. Lie Groups -- ยง 1. Background -- ยง2. Tangent Algebra -- ยง3. Connectedness and Simple Connectedness -- ยง 4. The Derived Algebra and the Radical -- 2. Algebraic Varieties -- ยง1. Affine Algebraic Varieties -- ยง 2. Projective and Quasiprojective Varieties -- ยง 3. Dimension and Analytic Properties of Algebraic Varieties -- 3. Algebraic Groups -- ยง 1. Background -- ยง2. Commutative and Solvable Algebraic Groups -- ยง 3. The Tangent Algebra -- ยง4. Compact Linear Groups -- 4. Complex Semisimple Lie Groups -- ยง1. Preliminaries -- ยง2. Root Systems -- ยง3. Existence and Uniqueness Theorems -- ยง4. Automorphisms -- 5. Real Semisimple Lie Groups -- ยง 1. Real Forms of Complex Semisimple Lie Groups and Algebras -- ยง 2. Compact Lie Groups and Reductive Algebraic Groups -- ยง 3. Cartan Decomposition -- ยง 4. Real Root Decomposition -- 6. Levi Decomposition -- 1ยฐ. Leviโs Theorem -- 2ยฐ. Existence of a Lie Group with the Given Tangent Algebra -- 3ยฐ. Malcevโs Theorem -- 4ยฐ. Algebraic Levi Decomposition -- Exercises -- Hints to Problems -- Reference Chapter -- ยง 1. Useful Formulae -- ยง2. Tables