Algebraic groups and differential Galois theory
By: Teresa Crespo, Zbigniew Hajto
Contributors: Hajto, Zbigniew
Series: Graduate studies in mathematics -- v. 122; Graduate studies in mathematics -- v. 122.
Publisher: American Mathematical Society
Published: 2011
Place of publication: Providence, R.I
Language: eng
Number of pages: 225
ISBN-13: 9780821853184
Subjects: Morphisms (Mathematics); Galois theory; Differential algebraic groups
Description: "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."--Publisher's description.
Notes: Includes bibliographical references and index.