**Graduate Studies in Mathematics**

Volume: 122;
2011;
225 pp;
Hardcover

MSC: Primary 12; 13; 14; 17; 20; 34; 68;

**Print ISBN: 978-0-8218-5318-4
Product Code: GSM/122**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-1-4704-1183-1
Product Code: GSM/122.E**

List Price: $56.00

AMS Member Price: $44.80

MAA Member Price: $50.40

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#### Supplemental Materials

# Algebraic Groups and Differential Galois Theory

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*Teresa Crespo; Zbigniew Hajto*

Differential Galois theory has seen intense
research activity during the last decades in several directions:
elaboration of more general theories, computational aspects, model
theoretic approaches, applications to classical and quantum mechanics
as well as to other mathematical areas such as number theory.

This book intends to introduce the reader to this subject by presenting
Picard-Vessiot theory, i.e. Galois theory of linear differential
equations, in a self-contained way. The needed prerequisites from
algebraic geometry and algebraic groups are contained in the first two
parts of the book. The third part includes Picard-Vessiot extensions, the
fundamental theorem of Picard-Vessiot theory, solvability by quadratures,
Fuchsian equations, monodromy group and Kovacic's algorithm. Over one
hundred exercises will help to assimilate the concepts and to introduce
the reader to some topics beyond the scope of this book.

This book is suitable for a graduate course in differential Galois theory.
The last chapter contains several suggestions for further reading
encouraging the reader to enter more deeply into different topics of
differential Galois theory or related fields.

#### Readership

Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.

#### Reviews & Endorsements

This well-crafted book certainly serves its intended purpose well: it is a very good self-contained introduction to Picard-Vessiot theory. ... It is a very nice book indeed.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## Algebraic Groups and Differential Galois Theory

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Introduction xiii14 free
- Part I. Algebraic geometry 116 free
- Affine and projective varieties 318
- Algebraic varieties 2742
- Part II. Algebraic groups 5368
- Basic notions 5570
- Lie algebras and algebraic groups 7590
- Part III. Differential Galois theory 119134
- Picard-Vessiot extensions 121136
- The Galois correspondence 141156
- Differential equations over ℂ(𝕫) 165180
- Suggestions for further reading 215230
- Bibliography 219234
- Index 223238 free
- Back Cover Back Cover1242