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Differential Algebraic Groups of Finite Dimension

  • Book
  • © 1992

Overview

Authors:
  1. Alexandru Buium
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1506)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XV
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  2. Terminology and conventions

    • Alexandru Buium
    Pages 1-6

  3. First properties

    • Alexandru Buium
    Pages 7-29

  4. Affine D-group schemes

    • Alexandru Buium
    Pages 30-59

  5. Commutative algebraic D-groups

    • Alexandru Buium
    Pages 60-86

  6. General algebraic D-groups

    • Alexandru Buium
    Pages 87-98

  7. Applications to differential algebraic groups

    • Alexandru Buium
    Pages 99-136

  8. Back Matter

    Pages 136-145
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Differential Algebraic Groups of Finite Dimension

  • Authors: Alexandru Buium

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0087235

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-55181-2Published: 26 February 1992

  • eBook ISBN: 978-3-540-46764-9Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVII, 147

  • Topics: Algebraic Geometry, Group Theory and Generalizations

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