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Author :
Publisher : Academic Press
ISBN 13 : 9780080873695
Total Pages : 446 pages
Book Rating : 4.93/5 ( download)
Download or read book Differential Algebra & Algebraic Groups written by and published by Academic Press. This book was released on 1973-06-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Algebra & Algebraic Groups
Author : E. R. Kolchin
Publisher :
ISBN 13 :
Total Pages : 446 pages
Book Rating : 4.64/5 ( download)
Download or read book Differential Algebra and Algebraic Groups written by E. R. Kolchin and published by . This book was released on 1973 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9814490504
Total Pages : 320 pages
Book Rating : 4.04/5 ( download)
Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration, and symmetry analysis of differential equations. This volume includes tutorial and survey papers presented at workshop. Contents:The Ritt–Kolchin Theory for Differential Polynomials (W Y Sit)Differential Schemes (J J Kovacic)Differential Algebra — A Scheme Theory Approach (H Gillet)Model Theory and Differential Algebra (T Scanlon)Inverse Differential Galois Theory (A R Magid)Differential Galois Theory, Universal Rings and Universal Groups (M van der Put)Cyclic Vectors (R C Churchill & J J Kovacic)Differential Algebraic Techniques in Hamiltonian Mechanics (R C Churchill)Moving Frames and Differential Algebra (E L Mansfield)Baxter Algebras and Differential Algebras (L Guo) Readership: Graduate students, pure mathematicians, logicians, algebraic geometers, applied mathematicians and physicists. Keywords:Differential Algebra;Mathematical Logic;Algebraic Geometry;Mathematical Physics
Author : Alexandru Buium
Publisher : Springer
ISBN 13 : 3540467645
Total Pages : 160 pages
Book Rating : 4.49/5 ( download)
Download or read book Differential Algebraic Groups of Finite Dimension written by Alexandru Buium and published by Springer. This book was released on 2006-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :
Publisher : Academic Press
ISBN 13 : 9780080874333
Total Pages : 272 pages
Book Rating : 4.39/5 ( download)
Download or read book Differential Algebraic Groups written by and published by Academic Press. This book was released on 1985-01-25 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Algebraic Groups
Author : Li Guo
Publisher : World Scientific
ISBN 13 : 9789810247034
Total Pages : 328 pages
Book Rating : 4.36/5 ( download)
Download or read book Differential Algebra and Related Topics written by Li Guo and published by World Scientific. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.
Author : Teresa Crespo
Publisher : American Mathematical Soc.
ISBN 13 : 082185318X
Total Pages : 242 pages
Book Rating : 4.84/5 ( download)
Download or read book Algebraic Groups and Differential Galois Theory written by Teresa Crespo and published by American Mathematical Soc.. This book was released on 2011 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Marius van der Put
Publisher : Springer Science & Business Media
ISBN 13 : 3642557503
Total Pages : 446 pages
Book Rating : 4.07/5 ( download)
Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author : J. S. Milne
Publisher : Cambridge University Press
ISBN 13 : 1107167485
Total Pages : 665 pages
Book Rating : 4.83/5 ( download)
Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author : J. S. Milne
Publisher : Cambridge University Press
ISBN 13 : 1316739155
Total Pages : 665 pages
Book Rating : 4.50/5 ( download)
Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti–Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.
