True Theory Of Representation
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| Author | : Pavel I. Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821853511 |
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 | : Gross Steven |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : |
| ISBN | : 9780198722199 |
| Author | : Hanna F. Pitkin |
| Publisher | : Univ of California Press |
| Total Pages | : 332 |
| Release | : 2023-04-28 |
| Genre | : Philosophy |
| ISBN | : 0520340507 |
Being concerned with representation, this book is about an idea, a concept, a word. It is primarily a conceptual analysis, not a historical study of the way in which representative government has evolved, nor yet an empirical investigation of the behavior of contemporary representatives or the expectations voters have about them. Yet, although the book is about a word, it is not about mere words, not merely about words. For the social philosopher, for the social scientist, words are not "mere"; they are the tools of his trade and a vital part of his subject matter. Since human beings are not merely political animals but also language-using animals, their behavior is shaped by their ideas. What they do and how they do it depends upon how they see themselves and their world, and this in turn depends upon the concepts through which they see. Learning what "representation" means and learning how to represent are intimately connected. But even beyond this, the social theorist sees the world through a network of concepts. Our words define and delimit our world in important ways, and this is particularly true of the world of human and social things. For a zoologist may capture a rare specimen and simply observe it; but who can capture an instance of representation (or of power, or of interest)? Such things, too, can be observed, but the observation always presupposes at least a rudimentary conception of what representation (or power, or interest) is, what counts as representation, where it leaves off and some other phenomenon begins. Questions about what representation is, or is like, are not fully separable from the question of what "representation" means. This book approaches the former questions by way of the latter. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972. Being concerned with representation, this book is about an idea, a concept, a word. It is primarily a conceptual analysis, not a historical study of the way in which representative government has evolved, nor yet an empirical investigation of the behavior
| Author | : Emmanuel Kowalski |
| Publisher | : American Mathematical Society |
| Total Pages | : 442 |
| Release | : 2014-08-28 |
| Genre | : Mathematics |
| ISBN | : 1470409666 |
Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
| Author | : William M. Ramsey |
| Publisher | : Cambridge University Press |
| Total Pages | : 284 |
| Release | : 2007-06-21 |
| Genre | : Philosophy |
| ISBN | : 9780521859875 |
| 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 | : James Nguyen |
| Publisher | : Cambridge University Press |
| Total Pages | : 154 |
| Release | : 2022-09-01 |
| Genre | : Science |
| ISBN | : 1009007343 |
This Element presents a philosophical exploration of the notion of scientific representation. It does so by focussing on an important class of scientific representations, namely scientific models. Models are important in the scientific process because scientists can study a model to discover features of reality. But what does it mean for something to represent something else? This is the question discussed in this Element. The authors begin by disentangling different aspects of the problem of representation and then discuss the dominant accounts in the philosophical literature: the resemblance view and inferentialism. They find them both wanting and submit that their own preferred option, the so-called DEKI account, not only eschews the problems that beset these conceptions, but further provides a comprehensive answer to the question of how scientific representation works. This title is also available as Open Access on Cambridge Core.
| 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 | : José L. Zalabardo |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 273 |
| Release | : 2015 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 0198743947 |
Jos L. Zalabardo puts forward a new interpretation of central ideas in Wittgenstein's Tractatus Logico-Philosophicus concerning the structure of reality and our representations of it in thought and language. He shows the origins of Wittgenstein's picture theory of propositional representation in Russell's theories of judgment, arguing that the picture theory is Wittgenstein's solution to some of the problems that he found in Russell's position. Zalabardo defends the view that, for Wittgenstein, facts in general, and the facts that play the role of propositions in particular, are not composite items, arising from the combination of their constituents. They are ultimate, irreducible units, and what we think of as their constituents are features that facts have in common with one another. These common features have built into them their possibilities of combination with other features into possible situations. This is the source of the Tractarian account of non-actual possibilities. It is also the source of the idea that it is not possible to produce propositions answering to certain descriptions, including those that would give rise to Russell's paradox. Zalabardo then considers Wittgenstein's view that every proposition is a truth function of elementary propositions. He argues that this view is motivated by Wittgenstein's epistemology of logic, according to which we should be able to see logical relations by inspecting the structures of propositions. Finally, Zalabardo considers the problems that we face if we try to extend the application of the picture theory from elementary propositions to truth functions of these.
| Author | : Robin Le Poidevin |
| Publisher | : Oxford University Press |
| Total Pages | : 210 |
| Release | : 2007-09-27 |
| Genre | : Philosophy |
| ISBN | : 0199265895 |
The Images of Time presents a philosophical investigation of the nature of time and the mind's ways of representing it. Robin Le Poidevin examines how we perceive time and change, the means by which memory links us with the past, the attempt to represent change and movement in art, and the nature of fictional time. These apparently disparate questions all concern the ways in which we represent aspects of time, in thought, experience, art and fiction. They also raisefundamental problems for our philosophical understanding, both of mental representation, and of the nature of time itself.Le Poidevin brings together issues in philosophy, psychology, aesthetics, and literary theory in examining the mechanisms underlying our representation of time in various media, and brings these to bear on metaphysical debates over the real nature of time. These debates concern which aspects of time are genuinely part of time's intrinsic nature, and which, in some sense, are mind-dependent.Arguably, the most important debate concerns time's passage: does time pass in reality, or is the division of events into past, present, and future simply a reflection of our temporal perspective - a result of the interaction between a 'static' world and minds capable of representing it? Le Poidevin argues that, contrary to what perception and memory lead us to suppose, time does not really pass, and this surprising conclusion can be reconciled with the characteristic features of temporalexperience.
