Introduction to Representation Theory
Introduction to Representation Theory

Author: Pavel I. Etingof

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 240

ISBN-13: 0821853511

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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.

Modes of Representation
Modes of Representation

Author: Richard Kimberly Heck

Publisher: Oxford University Press

Published: 2024-06-19

Total Pages: 444

ISBN-13: 0198861591

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Modes of Presentation analyses a collection of problems, known as 'Frege's puzzle', resulting from how thinkers and speakers have a limited perspective on reference in thought and language. Heck argues that these puzzles have much to teach us both about the foundations of cognition and the nature of linguistic communication.

The Musical Representation
The Musical Representation

Author: Charles O. Nussbaum

Publisher: MIT Press

Published: 2007

Total Pages: 401

ISBN-13: 0262140969

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How human musical experience emerges from the audition of organized tones is a riddle of long standing. In The Musical Representation, Charles Nussbaum offers a philosophical naturalist's solution. Nussbaum founds his naturalistic theory of musical representation on the collusion between the physics of sound and the organization of the human mind-brain. He argues that important varieties of experience afforded by Western tonal art music since 1650 arise through the feeling of tone, the sense of movement in musical space, cognition, emotional arousal, and the engagement, by way of specific emotional responses, of deeply rooted human ideals. Construing the art music of the modern West as representational, as a symbolic system that carries extramusical content, Nussbaum attempts to make normative principles of musical representation explicit and bring them into reflective equilibrium with the intuitions of competent listeners. Nussbaum identifies three modes of musical representation, describes the basis of extramusical meaning, and analyzes musical works as created historical entities (performances of which are tokens or replicas). In addition, he explains how music gives rise to emotions and evokes states of mind that are religious in character. Nussbaum's argument proceeds from biology, psychology, and philosophy to music--and occasionally from music back to biology, psychology, and philosophy. The human mind-brain, writes Nussbaum, is a living record of its evolutionary history; relatively recent cognitive acquisitions derive from older representational functions of which we are hardly aware. Consideration of musical art can help bring to light the more ancient cognitive functions that underlie modern human cognition. The biology, psychology, and philosophy of musical representation, he argues, have something to tell us about what we are, based on what we have been.

Quiver Representations
Quiver Representations

Author: Ralf Schiffler

Publisher: Springer

Published: 2014-09-04

Total Pages: 233

ISBN-13: 3319092049

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This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.

Society Of Mind
Society Of Mind

Author: Marvin Minsky

Publisher: Simon and Schuster

Published: 1988-03-15

Total Pages: 342

ISBN-13: 0671657135

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Computing Methodologies -- Artificial Intelligence.

Cameron Battle and the Hidden Kingdoms
Cameron Battle and the Hidden Kingdoms

Author: Jamar J. Perry

Publisher: Bloomsbury Publishing

Published: 2022-03-03

Total Pages: 323

ISBN-13: 1526646862

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Percy Jackson meets Black Panther - this blockbuster middle-grade fantasy adventure is perfect for fans of Amari and the Night Brothers. Cameron Battle grew up reading The Book of Chidani, cherishing stories about the fabled kingdom that cut itself off from the world to save the Igbo people from danger. Passed down over generations, the Book is Cameron's only connection to his parents, who disappeared one fateful night two years ago. Ever since, his grandmother has kept the Book locked away, but it calls to Cameron. When he and his best friends, Zion and Aliyah, decide to open it again, they are magically transported to Chidani. Instead of a land of beauty and wonder, they find a kingdom in extreme danger, as the queen's sister seeks to destroy the barrier between worlds. The people of Chidani have been waiting for the last Descendant to return and save them ... but is Cameron ready to be the hero they need? Inspired by West African and Igbo history and mythology, this adventure-filled fantasy introduces readers to Cameron Battle as he begins his journey to greatness.

Diagrammatic Representation and Inference
Diagrammatic Representation and Inference

Author: Gem Stapleton

Publisher: Springer

Published: 2008-09-22

Total Pages: 455

ISBN-13: 3540877304

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Diagrams is an international and interdisciplinary conference series, covering all aspects of research on the theory and application of diagrams. Recent technological advances have enabled the large-scale adoption of d- grams in a diverse range of areas. Increasingly sophisticated visual represen- tions are emerging and, to enable e?ective communication, insight is required into how diagrams are used and when they are appropriate for use. The per- sive, everyday use of diagrams for communicating information and ideas serves to illustrate the importance of providing a sound understanding of the role that diagrams can, and do, play. Research in the ?eld of diagrams aims to improve our understanding of the role of diagrams, sketches and other visualizations in communication, computation, cognition, creative thought, and problem solving. These concerns have triggered a surge of interest in the study of diagrams. The study of diagrammatic communication as a whole must be pursued as an interdisciplinary endeavour.Diagrams 2008 was the ?fth event in this conf- ence series, which was launched in Edinburghduring September 2000.Diagrams attracts a large number of researchers from virtually all related ?elds, placing the conference as a major international event in the area. Diagrams is the only conference that provides a united forum for all areas that are concerned with the study of diagrams: for example, architecture, - ti?cial intelligence, cartography, cognitive science, computer science, education, graphicdesign,historyofscience,human-computerinteraction,linguistics,logic, mathematics,philosophy,psychology,andsoftwaremodelling.Weseeissuesfrom all of these ?elds discussed in the papers collected in the present volume.

Representations of Algebras
Representations of Algebras

Author: Graham J. Leuschke

Publisher: American Mathematical Soc.

Published: 2018

Total Pages: 294

ISBN-13: 1470435764

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Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories.

Groups, Representations and Physics
Groups, Representations and Physics

Author: H.F Jones

Publisher: CRC Press

Published: 2020-07-14

Total Pages: 348

ISBN-13: 9781420050295

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Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.