Tensor Categories And Endomorphisms Of Von Neumann Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Tensor Categories And Endomorphisms Of Von Neumann Algebras PDF full book. Access full book title Tensor Categories And Endomorphisms Of Von Neumann Algebras.
| Author | : Marcel Bischoff |
| Publisher | : Springer |
| Total Pages | : 103 |
| Release | : 2015-01-13 |
| Genre | : Science |
| ISBN | : 3319143018 |
Download Tensor Categories and Endomorphisms of von Neumann Algebras Book in PDF, ePub and Kindle
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
| Author | : Sorin Popa |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803212 |
Download Classification of Subfactors and Their Endomorphisms Book in PDF, ePub and Kindle
This monograph provides a more unified and self-contained presentation of the results presented in Popa's earlier papers on this topic. The classification is in terms of the standard invariant $\mathcal G_{\mathcal N,\mathcal M}$ of the subfactor $\mathcal N\subset \mathcal M$. This invariant is a lattice of inclusions of finite dimensional algebras associated with the Jones iterated basic construction for $\mathcal N\subset \mathcal M$. ``Classification of Subfactors and Their Endomorphisms'' is based on lectures presented by Popa at the NSF-CBMS Regional Conference held in Eugene, Oregon, in August 1993.
| Author | : Pavel Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2016-08-05 |
| Genre | : Mathematics |
| ISBN | : 1470434415 |
Download Tensor Categories Book in PDF, ePub and Kindle
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
| Author | : Șerban Strătilă |
| Publisher | : Cambridge University Press |
| Total Pages | : 441 |
| Release | : 2019-05-09 |
| Genre | : Mathematics |
| ISBN | : 1108496849 |
Download Lectures on von Neumann Algebras Book in PDF, ePub and Kindle
The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
| Author | : Adrian Ocneanu |
| Publisher | : Springer |
| Total Pages | : 120 |
| Release | : 2006-12-08 |
| Genre | : Mathematics |
| ISBN | : 3540395792 |
Download Actions of Discrete Amenable Groups on von Neumann Algebras Book in PDF, ePub and Kindle
| Author | : Paul Bruillard |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2020-03-31 |
| Genre | : Education |
| ISBN | : 1470440741 |
Download Topological Phases of Matter and Quantum Computation Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24–25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments. The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.
| Author | : American Mathematical Society |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 258 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 082184881X |
Download Selected Papers on Analysis and Differential Equations Book in PDF, ePub and Kindle
"Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."
| Author | : Stephen Berman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 268 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821871447 |
Download Vertex Operator Algebras in Mathematics and Physics Book in PDF, ePub and Kindle
Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
| Author | : A. Katavolos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401155003 |
Download Operator Algebras and Applications Book in PDF, ePub and Kindle
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field. Among the topics treated are: operator spaces, Hilbert modules, limit algebras, reflexive algebras and subspaces, relations to basis theory, C* algebraic quantum groups, endomorphisms of operator algebras, conditional expectations and projection maps, and applications, particularly to wavelet theory. The volume also features an historical paper offering a new approach to the Pythagoreans' discovery of irrational numbers.
| Author | : Stephen Berman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 346 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821827162 |
Download Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory Book in PDF, ePub and Kindle
Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
