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Differential Algebraic Groups of Finite Dimension

  • Authors
  • Alexandru Buium

Part of the Lecture Notes in Mathematics book series (LNM, volume 1506)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Alexandru Buium
    Pages 1-6
  3. Alexandru Buium
    Pages 7-29
  4. Alexandru Buium
    Pages 30-59
  5. Alexandru Buium
    Pages 60-86
  6. Alexandru Buium
    Pages 87-98
  7. Alexandru Buium
    Pages 99-136
  8. Back Matter
    Pages 136-145

About this book

Introduction

Differential algebraic groups were introduced by P. Cassidy and E. Kolchin and are, roughly speaking, groups defined by algebraic differential equations in the same way as algebraic groups are groups defined by algebraic equations. The aim of the book is two-fold: 1) the provide an algebraic geometer's introduction to differential algebraic groups and 2) to provide a structure and classification theory for the finite dimensional ones. The main idea of the approach is to relate this topic to the study of: a) deformations of (not necessarily linear) algebraic groups and b) deformations of their automorphisms. The reader is assumed to possesssome standard knowledge of algebraic geometry but no familiarity with Kolchin's work is necessary. The book is both a research monograph and an introduction to a new topic and thus will be of interest to a wide audience ranging from researchers to graduate students.

Keywords

Dimension Grad algebraic geometry algebraic group commutative algebra

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0087235
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55181-2
  • Online ISBN 978-3-540-46764-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site