Representation Theory

Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Download or read book Representation Theory written by William Fulton and published by Springer Science & Business Media. This book was released on 1991 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Download or read book Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 1999 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The AMS History of Mathematics series is one of the most popular items for bookstore sales. These books feature colorful, attractive covers that are perfect for face out displays. The topics will appeal to a broad audience in the mathematical and scientific communities.

Download or read book A Tour of Representation Theory written by Martin Lorenz and published by American Mathematical Soc.. This book was released on 2018 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to four different flavours of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable the reader to pursue research in representation theory.

Download or read book Representation Theory written by Alexander Zimmermann and published by Springer. This book was released on 2014-08-15 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.