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.

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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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Table of contents (6 chapters)

Front Matter

Terminology and conventions

First properties

Affine D-group schemes

Commutative algebraic D-groups

General algebraic D-groups

Applications to differential algebraic groups

Back Matter

About this book