Introduction to Representation Theory PDF Download
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Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
ISBN: 0821853511
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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.
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
ISBN: 0821853511
Category : Mathematics
Languages : en
Pages : 240
Get Book Here
Book Description
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.
Author: Charles O. Nussbaum
Publisher: MIT Press
ISBN: 0262140969
Category : Emotions in music
Languages : en
Pages : 401
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Book Description
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.
Author: Richard Kimberly Heck
Publisher: Oxford University Press
ISBN: 0198861591
Category : Philosophy
Languages : en
Pages : 444
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Book Description
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.
Author: Ralf Schiffler
Publisher: Springer
ISBN: 3319092049
Category : Mathematics
Languages : en
Pages : 233
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Book Description
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.
Author: Tony Cliff
Publisher: First Second
ISBN: 1626726965
Category : Young Adult Fiction
Languages : en
Pages : 178
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Book Description
A NEW YORK TIMES BESTSELLER Lovable ne'er-do-well Delilah Dirk is an adventurer for the 19th century. She has traveled to Japan, Indonesia, France, and even the New World. Using the skills she's picked up on the way, Delilah's adventures continue as she plots to rob a rich and corrupt Sultan in Constantinople. With the aid of her flying boat and her newfound friend, Selim, she evades the Sultan's guards, leaves angry pirates in the dust, and fights her way through the countryside. For Delilah, one adventure leads to the next in this thrilling and funny installment in her exciting life. Tony Cliff's Delilah Dirk and the Turkish Lieutenant is a great pick for any reader looking for a smart and foolhardy heroine...and globetrotting adventures. A Publishers Weekly Best Children's Book of 2013 A Kirkus Reviews Best Teen Book of 2013
Author: H.F Jones
Publisher: CRC Press
ISBN: 9781420050295
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Jamar J. Perry
Publisher: Bloomsbury Publishing USA
ISBN: 1547606959
Category : Juvenile Fiction
Languages : en
Pages : 324
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Book Description
Inspired by West African and Igbo history and mythology, this adventurous middle-grade fantasy debut perfect for fans of Aru Shah and Tristan Strong celebrates the triumphs and challenges of a boy finding his truth path to greatness. As the true Descendant, I command to open The door to Chidani; it shall be broken Magic awaits those who seek the queen's peace And all the suffering you feel will cease Those who open the histories will hear a sound What was lost has finally been found. 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 . . . is Cameron ready to be the hero they need?
Author: Penelope Dean
Publisher: episode publishers
ISBN: 9789078525028
Category : Architectural design
Languages : en
Pages : 184
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Book Description
Author: Alexei Borodin
Publisher: Cambridge University Press
ISBN: 1107175550
Category : Mathematics
Languages : en
Pages : 169
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Book Description
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Author: Daniel H. Magilow
Publisher: Bloomsbury Publishing
ISBN: 1472513002
Category : History
Languages : en
Pages : 241
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Book Description
Holocaust Representations in History is an introduction to critical questions and debates surrounding the depiction, chronicling and memorialization of the Holocaust through the historical analysis of some of the most provocative and significant works of Holocaust representation. In a series of chronologically presented case studies, the book introduces the major themes and issues of Holocaust representation across a variety of media and genres, including film, drama, literature, photography, visual art, television, graphic novels, and memorials. The case studies presented not only include well-known, commercially successful, and canonical works about the Holocaust, such as the film Shoah and Elie Wiesel's memoir Night, but also controversial examples that have drawn accusations of profaning the memory of the genocide. Each work's specific historical and cultural significance is then discussed to provide further insight into the impact of one of the most devastating events of the 20th century and the continued relevance of its memory. Complete with illustrations, a bibliography and suggestions for further reading, key terms and discussion questions, this is an important book for any student keen to know more about the Holocaust and its impact.
