Affine Sets and Affine Groups (London Mathematical Society Lecture Note Series)

Northcott, D. G.

Cambridge University Press（1980/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 298 p.
• 言語 ENG
• 商品コード 9780521229098
• DDC分類 516.4

Full Description

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Contents

Introduction; Part I. Affine Sets: 1. Preliminaries concerning algebras; 2. Affine sets; 3. Irreducible affine sets; 4. Derivations and tangent spaces; Part II. Affine Groups: 5. Affine groups; 6. The associated Lie algebra; 7. Power series and exponentials; References; Index.