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A Journey Through Representation Theory
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Book Synopsis A Journey Through Representation Theory by : Caroline Gruson
Download or read book A Journey Through Representation Theory written by Caroline Gruson and published by Springer. This book was released on 2018-10-23 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
Book Synopsis A Tour of Representation Theory by : Martin Lorenz
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.
Book Synopsis Group Theory by : Predrag Cvitanović
Download or read book Group Theory written by Predrag Cvitanović and published by Princeton University Press. This book was released on 2008-07-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.
Book Synopsis Journeys Through Mental Illness by : Juliet Foster
Download or read book Journeys Through Mental Illness written by Juliet Foster and published by Bloomsbury Publishing. This book was released on 2018-06-26 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: At a time when service users' perspectives are increasingly recognized in healthcare, this seminal book highlights the importance of clients' perceptions of all aspects of mental illness. It examines the implications of these understandings, especially in relation to clients' relationships with services.
Book Synopsis A Journey through the History of Numerical Linear Algebra by : Claude Brezinski
Download or read book A Journey through the History of Numerical Linear Algebra written by Claude Brezinski and published by SIAM. This book was released on 2022-12-06 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Book Synopsis Operator Theory, Functional Analysis and Applications by : M. Amélia Bastos
Download or read book Operator Theory, Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.
Book Synopsis Group Matrices, Group Determinants and Representation Theory by : Kenneth W. Johnson
Download or read book Group Matrices, Group Determinants and Representation Theory written by Kenneth W. Johnson and published by Springer Nature. This book was released on 2019-11-08 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.
Download or read book Symmetry written by R. McWeeny and published by Elsevier. This book was released on 2013-09-03 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
Book Synopsis A Journey Through Time by : H G Tannhaus
Download or read book A Journey Through Time written by H G Tannhaus and published by . This book was released on 2020-04-20 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We trust in the linear, forever the same shape of the past, until eternity. But the diffrences between the past, presence and future are nothing but an illusion."
Book Synopsis The Mathematics of Frobenius in Context by : Thomas Hawkins
Download or read book The Mathematics of Frobenius in Context written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2013-07-23 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices.
Book Synopsis A Journey Through Discrete Mathematics by : Martin Loebl
Download or read book A Journey Through Discrete Mathematics written by Martin Loebl and published by Springer. This book was released on 2017-10-11 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.
Book Synopsis Semantics, Pragmatics, Philosophy by : Kasia M. Jaszczolt
Download or read book Semantics, Pragmatics, Philosophy written by Kasia M. Jaszczolt and published by Cambridge University Press. This book was released on 2023-03-31 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining semantics, pragmatics, and philosophy, this is a guide on how to think about meaning like a linguist and philosopher.
Book Synopsis Emergence of the Theory of Lie Groups by : Thomas Hawkins
Download or read book Emergence of the Theory of Lie Groups written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.
Book Synopsis Eva Figes' Writings by : Silvia Pellicer-Ortin
Download or read book Eva Figes' Writings written by Silvia Pellicer-Ortin and published by Cambridge Scholars Publishing. This book was released on 2015-10-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general overview of the life and literary career of the prolific writer Eva Figes, placing her extensive production within the various literary movements that have shaped the last century, and drawing on the main features of her works and the different stages in her production. Having recourse to the tools provided by narratology and using the theoretical background of the disciplines of ethics, Holocaust and trauma studies, together with other related fields such as theories of artistic representation, identity questions concerning Jewishness, contemporary history and philosophy, it carries out a comprehensive analysis of Figes’s main works. The main starting hypothesis explored throughout the book is that an evolution may be traced in the aesthetics employed by Figes throughout her career – from her initial Modernist phase to her more realist position – to depict individual and collective traumas. This development is a result of her need to find a mode of representing various traumatic events that have given shape to her personal and family history and to our recent collective history, from the two World Wars and the Holocaust to the social exclusion suffered by minority groups like women or the Jewish immigrant communities. This evolution will be also approached thematically, as there is a development from her early interest in depicting isolated male traumatised characters to the traumas suffered by women under patriarchal structures, and, then, to the encounter with her own suffering as a Holocaust survivor. The author’s evolution in the topics and narrative techniques employed mirrors the different stages in the individual and collective processes of recovery from traumatic experiences, from the process of acting out to the eventual healing phase. Thus, the conclusions detailed here will be useful not only to make Figes’ work known to a wider audience, but also to gain an insight into the evolution of the literary tendencies of the last few decades in trying to represent some of the most horrible events of the modern age.
Book Synopsis Sparse and Redundant Representations by : Michael Elad
Download or read book Sparse and Redundant Representations written by Michael Elad and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Journey through the Universe by : Ian Morison
Download or read book A Journey through the Universe written by Ian Morison and published by Cambridge University Press. This book was released on 2015 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date survey of our knowledge of the Universe beyond Earth, for general readers and astronomy enthusiasts.
Book Synopsis Linear Algebra Done Right by : Sheldon Axler
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
