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Author : Michael E. Burns
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.:/5 (34 download)
Download or read book Subfactors, Planar Algebras and Rotations written by Michael E. Burns and published by . This book was released on 2003 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Signorielli Penneys
Publisher :
ISBN 13 :
Total Pages : 145 pages
Book Rating : 4.:/5 (94 download)
Download or read book Planar Structure for Inclusions of Finite Von Neumann Algebras written by David Signorielli Penneys and published by . This book was released on 2012 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three self-contained papers from my graduate work at UC Berkeley. The chapters increase in complexity from the annular Temperley-Lieb category to strongly Markov inclusions of finite von Neumann algebras to infinite index II_1-subfactors. In Chapter 2, we discuss how two copies of the cyclic category generate the annular Temperley-Lieb category. In the process, we give a presentation of the annular Temperley-Lieb category via generators and relations, and we see the cyclic category evolve from the simplicial and semi-simplicial categories. Chapter 3 is joint work with Vaughan F.R. Jones. First, we define a canonical planar *-algebra associated to a strongly Markov inclusion of finite von Neumann algebras (the notion of such an inclusion is defined within). Second, we show for an inclusion of finite dimensional C^*-algebras with the Markov trace, the canonical planar algebra is isomorphic to the graph planar algebra of the Bratteli diagram of the inclusion. We use this fact to show that a subfactor planar algebra embeds into the graph planar algebra of its principal graph. In Chapter 4, we expand upon Burns' work on rotations for infinite index II_1-subfactors. We start with a II_1-factor bimodule, and we construct a tower of centralizer algebras and a sequence of central L^2-vectors. In the finite index setting, the centralizer algebras and central L^2-vectors agree, but in the infinite index setting, these spaces can differ dramatically. We develop planar calculi for both sequences which are compatible. Interestingly, we obtain planar structure without Jones' basic construction or the resulting Jones projections! We also generalize Burns work on extremality and the existence of rotations to the bimodule setting, and we recover his main theorem. Along the way, we prove some results about relative tensor products of extended positive cones, and we give an example of an infinite index subfactor with finite dimensional higher relative commutants.
Author : Narjess Afzaly
Publisher : American Mathematical Society
ISBN 13 : 1470447126
Total Pages : 94 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Classification of Subfactors with Index at Most $5 frac {1}{4}$ written by Narjess Afzaly and published by American Mathematical Society. This book was released on 2023-04-07 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1001 pages
Book Rating : 4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zeph A. Landau
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (34 download)
Download or read book Intermediate Subfactors written by Zeph A. Landau and published by . This book was released on 1998 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Institut des hautes études scientifiques (Paris, France)
Publisher : American Mathematical Soc.
ISBN 13 : 0821852035
Total Pages : 695 pages
Book Rating : 4.8/5 (218 download)
Download or read book Quanta of Maths written by Institut des hautes études scientifiques (Paris, France) and published by American Mathematical Soc.. This book was released on 2010 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.
Author : Paul Bruillard
Publisher : American Mathematical Soc.
ISBN 13 : 1470440741
Total Pages : 240 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topological Phases of Matter and Quantum Computation written by Paul Bruillard and published by American Mathematical Soc.. This book was released on 2020-03-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher :
ISBN 13 :
Total Pages : 806 pages
Book Rating : 4.3/5 (91 download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xiangping Huang
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (34 download)
Download or read book Commutators Associated to a Subfactor and Its Relative Commutants written by Xiangping Huang and published by . This book was released on 2000 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vaughan F. R. Jones
Publisher : Cambridge University Press
ISBN 13 : 0521584205
Total Pages : 178 pages
Book Rating : 4.5/5 (215 download)
Download or read book Introduction to Subfactors written by Vaughan F. R. Jones and published by Cambridge University Press. This book was released on 1997-05-15 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subfactors have been a subject of considerable research activity for about 15 years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late ch apter.
Author :
Publisher :
ISBN 13 :
Total Pages : 1078 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bina Bhattacharyya
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (34 download)
Download or read book Krishnan-Sunder Subfactors and a New Countable Family of Subfactors Related to Trees written by Bina Bhattacharyya and published by . This book was released on 1998 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Noah Joseph Snyder
Publisher :
ISBN 13 :
Total Pages : 410 pages
Book Rating : 4.:/5 (35 download)
Download or read book Quantum Groups, Tensor Categories, and Knot Invariants written by Noah Joseph Snyder and published by . This book was released on 2009 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Volodymyr Nekrashevych
Publisher : American Mathematical Soc.
ISBN 13 : 0821838318
Total Pages : 248 pages
Book Rating : 4.8/5 (218 download)
Download or read book Self-Similar Groups written by Volodymyr Nekrashevych and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.
Author : Colin C. Adams
Publisher : Springer
ISBN 13 : 3030160319
Total Pages : 476 pages
Book Rating : 4.0/5 (31 download)
Download or read book Knots, Low-Dimensional Topology and Applications written by Colin C. Adams and published by Springer. This book was released on 2019-06-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.
Author : James A. Mingo
Publisher : Springer
ISBN 13 : 1493969420
Total Pages : 343 pages
Book Rating : 4.4/5 (939 download)
Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
