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Author: Harm Derksen
Publisher: American Mathematical Soc.
ISBN: 1470425564
Category : Mathematics
Languages : en
Pages : 346
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Book Description
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.
Author: Harm Derksen
Publisher: American Mathematical Soc.
ISBN: 1470425564
Category : Mathematics
Languages : en
Pages : 346
Get Book Here
Book Description
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.
Author: A. A. Kirillov
Publisher: Springer Science & Business Media
ISBN: 3642662439
Category : Mathematics
Languages : en
Pages : 327
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Book Description
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.
Author: Stuart Hall
Publisher: SAGE
ISBN: 9780761954323
Category : Business & Economics
Languages : en
Pages : 422
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Book Description
This broad-ranging text offers a comprehensive outline of how visual images, language and discourse work as `systems of representation'. Individual chapters explore: representation as a signifying practice in a rich diversity of social contexts and institutional sites; the use of photography in the construction of national identity and culture; other cultures in ethnographic museums; fantasies of the racialized `Other' in popular media, film and image; the construction of masculine identities in discourses of consumer culture and advertising; and the gendering of narratives in television soap operas.
Author: Umberto Eco
Publisher: Indiana University Press
ISBN: 9780253337245
Category : Semantics
Languages : en
Pages : 252
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Book Description
..". an excellent collection... " -- Journal of Language Social Psychology An important collection of original essays by well-known scholars debating the questions of logical versus psychologically-based interpretations of language.
Author: Michael Elad
Publisher: Springer Science & Business Media
ISBN: 1441970118
Category : Mathematics
Languages : en
Pages : 376
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Book Description
A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.
Author: Alexander Kirillov Jr.
Publisher: American Mathematical Soc.
ISBN: 1470423073
Category : Mathematics
Languages : en
Pages : 311
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Book Description
This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac–Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many examples make the book accessible to graduate students who want to learn about quivers, their representations, and their relations to algebraic geometry and Lie algebras.
Author: William Fulton
Publisher: Springer Science & Business Media
ISBN: 9780387974958
Category : Mathematics
Languages : en
Pages : 616
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Book Description
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.
Author: Jerry A. Fodor
Publisher: MIT Press
ISBN: 0262560275
Category : Psychology
Languages : en
Pages : 357
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Book Description
These essays will shape discussion in the philosophy of psychology for years to come. A collection of eleven essays dealing with methodological and empirical issues in cognitive science and in the philosophy of mind, Representations convincingly connects philosophical speculation to concrete empirical research.One of the outstanding methodological issues dealt with is the status of functionalism considered as an alternative to behavioristic and physicalistic accounts. of mental states and properties. The other issue is the status of reductionism considered as an account of the relation between the psychological and physical sciences. The first chapters present the main lines of argument which have made functionalism the currently favored philosophical approach to ontology of the mental.The outlines of a psychology of propositional attitudes which emerges from consideration of current developments in cognitive science are contained in the remaining essays.Not all of these essays are re-presentations. The new introductory essay seeks to present an overview and gives some detailed proposals about the contribution that functionalism makes to the solutions of problems about intentionality. The concluding essay, also not previously published, is a sustained examination of the relation between theories about the structure of concepts and theories about how they are learned. Finally, the essay "Three cheers for propositional attitudes", a critical examination of some of D. C. Dennett's ideas, has been completely rewritten for this volume. A Bradford Book.
Author: Julie Barnes
Publisher: MAA Press
ISBN: 9780883855911
Category :
Languages : en
Pages : 40
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Book Description
Have you ever seen a mathematical object that was so intriguing that anyone, regardless of mathematical background, could appreciate its aesthetic beauty? If so, did you stop to color it? Now is your chance. Explore the beauty of mathematics in this collection if intricate pictures related to complex-valued functions. Any of these images could pass for designs found in some of the many coloring books for adults seen in stores today and are displayed here for you to color. While looking at the coloring pages, you can read about the author's quest to find interesting images. Their tale includes expeditions on the complex plane, work with families of complex functions, visits to Julia sets, unexpected results from a typo, random explorations, and a final send-off from a well-known cartoon character. Grab your colored pencils and enjoy coloring these functions. There are no incorrect ways to color, and consequently, there are no answers in the back of the book!
Author: Jean-Pierre Serre
Publisher: CRC Press
ISBN: 1439863865
Category : Mathematics
Languages : en
Pages : 203
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Book Description
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
