A Journey Through Representation Theory
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Author | : Caroline Gruson |
Publisher | : Springer |
Total Pages | : 231 |
Release | : 2018-10-23 |
Genre | : Mathematics |
ISBN | : 3319982710 |
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.
Author | : Martin Lorenz |
Publisher | : American Mathematical Soc. |
Total Pages | : 674 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 1470436809 |
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.
Author | : Claude Brezinski |
Publisher | : SIAM |
Total Pages | : 813 |
Release | : 2022-12-06 |
Genre | : Mathematics |
ISBN | : 1611977231 |
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.
Author | : M. Amélia Bastos |
Publisher | : Springer Nature |
Total Pages | : 654 |
Release | : 2021-03-31 |
Genre | : Mathematics |
ISBN | : 3030519457 |
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.
Author | : Kenneth W. Johnson |
Publisher | : Springer Nature |
Total Pages | : 384 |
Release | : 2019-11-08 |
Genre | : Mathematics |
ISBN | : 3030283003 |
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.
Author | : Michael Elad |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2010-08-12 |
Genre | : Mathematics |
ISBN | : 1441970118 |
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 | : Thomas Hawkins |
Publisher | : Springer Science & Business Media |
Total Pages | : 698 |
Release | : 2013-07-23 |
Genre | : Mathematics |
ISBN | : 1461463335 |
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.
Author | : Vinaya Manchaiah |
Publisher | : Routledge |
Total Pages | : 197 |
Release | : 2019-05-30 |
Genre | : Social Science |
ISBN | : 135100364X |
Disability and Social Representations Theory provides theoretical and methodological knowledge to uncover the public perception of disabilities. Over the last decade there has been a significant shift from body to environment, and the relation between the two, when understanding the phenomenon of disabilities. The current trend is to view disabilities as the outcome of this interaction; in short from a biopsychosocial perspective. This has called for research based on frameworks that incorporate both the body and the environment. There is a great corpus of knowledge of the functions of a body, and a growing corpus of environmental factors such as perceptions among specific groups of persons towards disabilities. However, there is a lack of knowledge of the perception of disabilities from a general population. This book offers an insight into how we can broaden our understanding of disability by using Social Representations Theory, with specific examples from studies on hearing loss. The authors highlight that attitudes and actions are outcomes of a more fundamental disposition (i.e., social representation) towards a phenomenon like disability. This book is written assuming the reader has no prior knowledge of Social Representations Theory. It will be of interest to all scholars, students and professionals working in the fields of disability studies, health and social care, and sociology.
Author | : Kasia M. Jaszczolt |
Publisher | : Cambridge University Press |
Total Pages | : 439 |
Release | : 2023-03-31 |
Genre | : Language Arts & Disciplines |
ISBN | : 1108499651 |
Combining semantics, pragmatics, and philosophy, this is a guide on how to think about meaning like a linguist and philosopher.
Author | : Jing-Song Huang |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2007-05-27 |
Genre | : Mathematics |
ISBN | : 0817644938 |
This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.