A Journey Through Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Journey Through Representation Theory write by Caroline Gruson. This book was released on 2018-10-23. A Journey Through Representation Theory available in PDF, EPUB and Kindle. 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.
A Tour of Representation Theory
A Tour of Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Tour of Representation Theory write by Martin Lorenz. This book was released on 2018. A Tour of Representation Theory available in PDF, EPUB and Kindle. 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.
Group Theory
Group Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Group Theory write by Predrag Cvitanović. This book was released on 2008-07-01. Group Theory available in PDF, EPUB and Kindle. 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.
A Journey through the History of Numerical Linear Algebra
A Journey through the History of Numerical Linear Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Journey through the History of Numerical Linear Algebra write by Claude Brezinski . This book was released on 2022-12-06. A Journey through the History of Numerical Linear Algebra available in PDF, EPUB and Kindle. 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.
Operator Theory, Functional Analysis and Applications
Operator Theory, Functional Analysis and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Theory, Functional Analysis and Applications write by M. Amélia Bastos. This book was released on 2021-03-31. Operator Theory, Functional Analysis and Applications available in PDF, EPUB and Kindle. 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.
