Differential Tensor Algebras And Their Module Categories
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Author | : R. Bautista |
Publisher | : Cambridge University Press |
Total Pages | : 463 |
Release | : 2009-09-17 |
Genre | : Mathematics |
ISBN | : 0521757681 |
A detailed account of main results in the theory of differential tensor algebras.
Author | : Pavel Etingof |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2016-08-05 |
Genre | : Mathematics |
ISBN | : 1470434415 |
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 | : Chengming Bai |
Publisher | : Springer Science & Business Media |
Total Pages | : 285 |
Release | : 2013-10-30 |
Genre | : Mathematics |
ISBN | : 3642393837 |
The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Author | : Peter H. Kropholler |
Publisher | : Cambridge University Press |
Total Pages | : 277 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 131662322X |
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Author | : Society for the Foundation of Computational Mathematics |
Publisher | : Cambridge University Press |
Total Pages | : 249 |
Release | : 2013 |
Genre | : Computers |
ISBN | : 1107604079 |
A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.
Author | : John van der Hoek |
Publisher | : Cambridge University Press |
Total Pages | : 186 |
Release | : 2018-02-08 |
Genre | : Mathematics |
ISBN | : 1108383904 |
Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.
Author | : Pierre-Emmanuel Caprace |
Publisher | : Cambridge University Press |
Total Pages | : 367 |
Release | : 2018-02-08 |
Genre | : Mathematics |
ISBN | : 1108349544 |
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.
Author | : Wolfgang Metzler |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 1316600904 |
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Author | : Javier Esparza |
Publisher | : Cambridge University Press |
Total Pages | : 355 |
Release | : 2011-03-10 |
Genre | : Computers |
ISBN | : 0521718201 |
Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Author | : James Cummings |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 2012-11-15 |
Genre | : Mathematics |
ISBN | : 1107608503 |
Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.