Algebraic and Analytic Methods in Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic and Analytic Methods in Representation Theory write by . This book was released on 1996-09-27. Algebraic and Analytic Methods in Representation Theory available in PDF, EPUB and Kindle. This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field
Representation Theory of Finite Groups: Algebra and Arithmetic
Representation Theory of Finite Groups: Algebra and Arithmetic - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory of Finite Groups: Algebra and Arithmetic write by Steven H. Weintraub. This book was released on 2003. Representation Theory of Finite Groups: Algebra and Arithmetic available in PDF, EPUB and Kindle. ``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.
Representation Theory of Algebraic Groups and Quantum Groups
Representation Theory of Algebraic Groups and Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation Theory of Algebraic Groups and Quantum Groups write by Toshiaki Shoji. This book was released on 2004. Representation Theory of Algebraic Groups and Quantum Groups available in PDF, EPUB and Kindle. A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.
Analytic, Algebraic and Geometric Aspects of Differential Equations
Analytic, Algebraic and Geometric Aspects of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic, Algebraic and Geometric Aspects of Differential Equations write by Galina Filipuk. This book was released on 2017-06-23. Analytic, Algebraic and Geometric Aspects of Differential Equations available in PDF, EPUB and Kindle. This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
Introduction to Lie Algebras and Representation Theory
Introduction to Lie Algebras and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Lie Algebras and Representation Theory write by J.E. Humphreys. This book was released on 2012-12-06. Introduction to Lie Algebras and Representation Theory available in PDF, EPUB and Kindle. This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
