Linear Algebraic Groups

1. Front Matter

   Pages i-xi

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2. Background Material from Algebraic Geometry

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   Pages 1-45

3. General Notions Associated With Algebraic Groups

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   Pages 46-88

4. Homogeneous Spaces

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   Pages 89-110

5. Solvable Groups

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   Pages 111-146

6. Borel Subgroups; Reductive Groups

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   Pages 147-202

7. Rationality Questions

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   Pages 203-279

8. Back Matter

   Pages 280-290

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This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over non-algebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs.

• Lie algebra
• algebra
• algebraic group
• commutative algebra
• linear algebra

• School of Mathematics, Institute for Advanced Study, Princeton, USA

  Armand Borel

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