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Lectures on Differential Galois Theory
Andy R. Magid, University of Oklahoma, Norman, OK
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University Lecture Series
1994; 105 pp; softcover
Volume: 7
Reprint/Revision History:
reprinted with corrections 1997
ISBN-10: 0-8218-7004-1
ISBN-13: 978-0-8218-7004-4
List Price: US$23
Member Price: US$18.40
Order Code: ULECT/7
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See also:

Algebraic Groups and Differential Galois Theory - Teresa Crespo and Zbigniew Hajto

Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solutions of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a self-contained development and many explicit examples, this book provides a unique approach to differential Galois theory and is suitable as a textbook at the advanced graduate level.

Readership

Graduate students and researchers.

Reviews

"The present book offers an elegant alternative approach to the Galois theory of linear homogeneous differential equations, based on the principle that the Galois correspondence should be obtained as a consequence of the algebraic group-theoretic construction of Picard-Vessiot extensions."

-- Mathematical Reviews

"The self-contained introduction Magid's 100-page book provides should help the newcomer to proceed further into this beautiful and active field."

-- Bulletin of the AMS

Table of Contents

  • Differential ideals
  • The Wronskian
  • Picard-Vessiot extensions
  • Automorphisms of Picard-Vessiot extensions
  • The structure of Picard-Vessiot extensions
  • The Galois correspondence and its consequences
  • The inverse Galois problem
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