Affine Sets and Affine Groups

D. G. Northcott

doi:10.1017/CBO9781107325456

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.

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Affine Sets and Affine Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-x

PART I - AFFINE SETS
pp 1-2

Chapter 1 - Preliminaries concerning algebras
pp 3-11

Chapter 2 - Affine sets
pp 12-59

Chapter 3 - Irreducible affine sets
pp 60-94

Chapter 4 - Derivations and tangent spaces
pp 95-130

PART II - AFFINE GROUPS
pp 131-132

Chapter 5 - Affine groups
pp 133-221

Chapter 6 - The associated Lie algebra
pp 222-262

Chapter 7 - Power series and exponentials
pp 263-282

References
pp 283-283

Index
pp 284-285

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