Download or read book Basic Representation Theory of Algebras written by Ibrahim Assem and published by Springer Nature. This book was released on 2020-04-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
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 Basis of Representation Review written by Hill, Young, Cooper and published by . This book was released on 2005 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basis of Representation written by Thaddeus Stevens and published by . This book was released on 1866 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representations and Cohomology Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras written by D. J. Benson and published by Cambridge University Press. This book was released on 1998-06-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to modern developments in the representation theory of finite groups and associative algebras.
Download or read book Algorithmic Foundation of Multi Scale Spatial Representation written by Zhilin Li and published by CRC Press. This book was released on 2006-10-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. However, no book to date has systematically tackled the different aspects of this discipline. Emphasizing map generalization, Algorithmic Foundation of Multi-Scale Spatial Representation addresses the mathematical basis of
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 Reconsidered written by William M. Ramsey and published by Cambridge University Press. This book was released on 2007-06-21 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description
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 The Concept of Representation written by Hanna F. Pitkin and published by Univ of California Press. This book was released on 2023-04-28 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Being concerned with representation, this book is about an idea, a concept, a word. It is primarily a conceptual analysis, not a historical study of the way in which representative government has evolved, nor yet an empirical investigation of the behavior of contemporary representatives or the expectations voters have about them. Yet, although the book is about a word, it is not about mere words, not merely about words. For the social philosopher, for the social scientist, words are not "mere"; they are the tools of his trade and a vital part of his subject matter. Since human beings are not merely political animals but also language-using animals, their behavior is shaped by their ideas. What they do and how they do it depends upon how they see themselves and their world, and this in turn depends upon the concepts through which they see. Learning what "representation" means and learning how to represent are intimately connected. But even beyond this, the social theorist sees the world through a network of concepts. Our words define and delimit our world in important ways, and this is particularly true of the world of human and social things. For a zoologist may capture a rare specimen and simply observe it; but who can capture an instance of representation (or of power, or of interest)? Such things, too, can be observed, but the observation always presupposes at least a rudimentary conception of what representation (or power, or interest) is, what counts as representation, where it leaves off and some other phenomenon begins. Questions about what representation is, or is like, are not fully separable from the question of what "representation" means. This book approaches the former questions by way of the latter. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972. Being concerned with representation, this book is about an idea, a concept, a word. It is primarily a conceptual analysis, not a historical study of the way in which representative government has evolved, nor yet an empirical investigation of the behavior
Download or read book Representation of Universal Algebra written by Aleks Kleyn and published by CreateSpace. This book was released on 2015-04-06 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more general point of view I started the book from consideration of Cartesian product of representations. Polymorphism of representations is a map of Cartesian product of representations which is a morphism of representations with respect to each separate independent variable. Reduced morphism of representations allows us to simplify the study of morphisms of representations. However a representation has to satisfy specific requirements for existence of reduced polymomorphism of representations. It is possible that Abelian group is only Ω-algebra, such that representation in this algebra admits polymorphism of representations. However, today, this statement has not been proved. Multiplicative Ω-group is Ω-algebra in which product is defined. The definition of tensor product of representations of Abelian multiplicative Ω-group is based on properties of reduced polymorphism of representations of Abelian multiplicative Ω-group. Since algebra is a module in which the product is defined, then we can use this theory to study linear map of algebra. For instance, we can study the set of linear transformations of D-algebra A as representation of algebra A⊗A in algebra A.
Download or read book Algebras and Representation Theory written by Karin Erdmann and published by Springer. This book was released on 2018-09-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
Download or read book The Social Basis of Proportional Representation written by Jeremiah Whipple Jenks and published by . This book was released on 1895 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basis of Representation written by George Stillman Hillard and published by . This book was released on 1853 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representation Theorems in Computer Science written by Özgür Lütfü Özçep and published by Springer. This book was released on 2019-07-16 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal specifications are an important tool for the construction, verification and analysis of systems, since without it is hardly possible to explain whether a system worked correctly or showed an expected behavior. This book proposes the use of representation theorems as a means to develop an understanding of all models of a specification in order to exclude possible unintended models, demonstrating the general methodology with representation theorems for applications in qualitative spatial reasoning, data stream processing, and belief revision. For qualitative spatial reasoning, it develops a model of spatial relatedness that captures the scaling context with hierarchical partitions of a spatial domain, and axiomatically characterizes the resulting relations. It also shows that various important properties of stream processing, such as prefix-determinedness or various factorization properties can be axiomatized, and that the axioms are fulfilled by natural classes of stream functions. The third example is belief revision, which is concerned with the revision of knowledge bases under new, potentially incompatible information. In this context, the book considers a subclass of revision operators, namely the class of reinterpretation operators, and characterizes them axiomatically. A characteristic property of reinterpretation operators is that of dissolving potential inconsistencies by reinterpreting symbols of the knowledge base. Intended for researchers in theoretical computer science or one of the above application domains, the book presents results that demonstrate the use of representation theorems for the design and evaluation of formal specifications, and provide the basis for future application-development kits that support application designers with automatically built representations.
Download or read book Elements of the Representation Theory of the Jacobi Group written by Rolf Berndt and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.
Download or read book The Concept of Constituency written by Andrew Rehfeld and published by Cambridge University Press. This book was released on 2005-06-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: In virtually every democratic nation in the world, political representation is defined by where citizens live. In the United States, for example, Congressional Districts are drawn every 10 years as lines on a map. Why do democratic governments define political representation this way? Are territorial electoral constituencies commensurate with basic principles of democratic legitimacy? And why might our commitments to these principles lead us to endorse a radical alternative: randomly assigning citizens to permanent, single-member electoral constituencies that each looks like the nation they collectively represent? Using the case of the founding period of the United States as an illustration, and drawing from classic sources in Western political theory, this book describes the conceptual, historical, and normative features of the electoral constituency. As an institution conceptually separate from the casting of votes, the electoral constituency is little studied. Its historical origins are often incorrectly described. And as a normative matter, the constituency is almost completely ignored. Raising these conceptual, historical and normative issues, the argument culminates with a novel thought experiment of imagining how politics might change under randomized, permanent, national electoral constituencies. By focusing on how citizens are formally defined for the purpose of political representation, The Concept of Constituency thus offers a novel approach to the central problems of political representation, democratic legitimacy, and institutional design.
