Download or read book Graphical Calculus on Representations of Quantum Lie Algebras written by Dongseok Kim and published by . This book was released on 2003 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Download or read book A Diagrammatic Category for the Representation Theory of Uq sin written by Scott Edward Morrison and published by . This book was released on 2007 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2003 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extended Graphical Calculus for Categorified Quantum sl 2 written by Mikhail Khovanov and published by American Mathematical Soc.. This book was released on 2012 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an earlier paper, Aaron D. Lauda constructed a categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2); here he, Khovanov, Marco Mackaay, and Marko Stosic enhance the graphical calculus he introduced to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms, which are in a bijection with the Lusztig canonical basis elements. Their results show that one of Lauda's main results holds when the 2-category is defined over the ring of integers rather than over a field. The study is not indexed. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Download or read book Perspectives in Representation Theory written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2014-03-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honor of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and -adic groups, and quantum gauge theories. The papers in this volume present representation theory connections to numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.
Download or read book Iwahori Hecke Algebras and Schur Algebras of the Symmetric Group written by Andrew Mathas and published by American Mathematical Soc.. This book was released on 1999 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.
Download or read book Lie Algebras Lie Superalgebras Vertex Algebras and Related Topics written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.
Download or read book Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2004-11-15 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Quantum Groups written by Petr P. Kulish and published by Springer. This book was released on 2007-02-08 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.
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:
Download or read book String Math 2022 written by Ron Donagi and published by American Mathematical Society. This book was released on 2024-04-18 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a proceedings volume from the String-Math conference which took place at the University of Warsaw in 2022. This 12th String-Math conference focused on several research areas actively developing these days. They included generalized (categorical) symmetries in quantum field theory and their relation to topological phases of matter; formal aspects of quantum field theory, in particular twisted holography; various developments in supersymmetric gauge theories, BPS counting and Donaldson–Thomas invariants. Other topics discussed at this conference included new advances in Gromov–Witten theory, curve counting, and Calabi–Yau manifolds. Another broad topic concerned algebraic aspects of conformal field theory, vertex operator algebras, and quantum groups. Furthermore, several other recent developments were presented during the conference, such as understanding the role of operator algebras in the presence of gravity, derivation of gauge-string duality, complexity of black holes, or mathematical aspects of the amplituhedron. This proceedings volume contains articles summarizing 14 conference lectures, devoted to the above topics.
Download or read book Lectures on Tensor Categories and Modular Functors written by Bojko Bakalov and published by American Mathematical Soc.. This book was released on 2001 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.
Download or read book Planar Algebras in Braided Tensor Categories written by André Gil Henriques and published by American Mathematical Society. This book was released on 2023-02-13 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Topological Quantum Computation written by Zhenghan Wang and published by American Mathematical Soc.. This book was released on 2010 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Download or read book Quantum Topology Proceedings Of The Conference written by David N Yetter and published by World Scientific. This book was released on 1994-08-19 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the conference on quantum topology, held at Kansas State University, Manhattan, KS, 24 - 28 March 1993.Quantum topology is a rapidly growing field of mathematics dealing with the recently discovered interactions between low-dimensional topology, the theory of quantum groups, category theory, C∗-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics. The conference, attended by over 60 mathematicians and theoretical physicists from Canada, Denmark, England, France, Japan, Poland and the United States, was highlighted by lecture series given by Louis Kauffman, Univ. of Illinois at Chicago and Nicholai Reshetikhin, Univ. of Califonia, Berkeley.
