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Algebraic Groups and Differential Galois Theory

Teresa Crespo Universitat de Barcelona, Barcelona, Spain
Zbigniew Hajto Jagiellonian University, Kraków, Poland
Available Formats:
Hardcover ISBN: 978-0-8218-5318-4
Product Code: GSM/122
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $48.00 Electronic ISBN: 978-1-4704-1183-1 Product Code: GSM/122.E List Price:$56.00
MAA Member Price: $50.40 AMS Member Price:$44.80
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List Price: $90.00 MAA Member Price:$81.00
AMS Member Price: $72.00 Click above image for expanded view Algebraic Groups and Differential Galois Theory Teresa Crespo Universitat de Barcelona, Barcelona, Spain Zbigniew Hajto Jagiellonian University, Kraków, Poland Available Formats:  Hardcover ISBN: 978-0-8218-5318-4 Product Code: GSM/122  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$48.00
 Electronic ISBN: 978-1-4704-1183-1 Product Code: GSM/122.E
 List Price: $56.00 MAA Member Price:$50.40 AMS Member Price: $44.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$90.00 MAA Member Price: $81.00 AMS Member Price:$72.00
• Book Details

Volume: 1222011; 225 pp
MSC: Primary 12; 13; 14; 17; 20; 34; 68;

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.

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

• Part 1. Algebraic geometry
• Chapter 1. Affine and projective varieties
• Chapter 2. Algebraic varieties
• Part 2. Algebraic groups
• Chapter 3. Basic notions
• Chapter 4. Lie algebras and algebraic groups
• Part 3. Differential Galois theory
• Chapter 5. Picard-Vessiot extensions
• Chapter 6. The Galois correspondence
• Chapter 7. Differential equations over $\mathbb {C}(z)$
• Chapter 8. Suggestions for further reading

• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1222011; 225 pp
MSC: Primary 12; 13; 14; 17; 20; 34; 68;

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.

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

• Part 1. Algebraic geometry
• Chapter 1. Affine and projective varieties
• Chapter 2. Algebraic varieties
• Part 2. Algebraic groups
• Chapter 3. Basic notions
• Chapter 4. Lie algebras and algebraic groups
• Part 3. Differential Galois theory
• Chapter 5. Picard-Vessiot extensions
• Chapter 6. The Galois correspondence
• Chapter 7. Differential equations over $\mathbb {C}(z)$
• Chapter 8. Suggestions for further reading
• 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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