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.
This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the U.S. Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups. The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.
This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
This monograph provides a more unifed and self-contained presentation of the results presented in Popa's earlier papers on this topic. "Classifications 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.
Digital Business Transformation, Digitalisation, Business Strategy, Business Process, Business Analysis, Business Architecture, Business Models This book serves practitioners as a guide to digital business engineering. It was consciously conceived and prepared from a methodological perspective, thereby avoiding a strongly "technological" approach, rather focusing on the presentation of methods and instruments. Its basis is a tried and tested framework model that can be understood as the ideal management cycle of digital business engineering. The control loop consists of goal-setting (Chapter 1: Setting a Business Strategy), implementation (Chapters 2–5), and success assessment (Chapter 6: Validating the Success of Business Transformation) and is located in an outer circuit. The operational implementation phases of digital business engineering are part of the inner cycle: Defining a Business Case (Chapter 2), Eliciting the Business Processes (Chapter 3), Deriving the Business Requirements (Chapter 4), and Transforming the Business Architecture (Chapter 5). The book follows a didactic structure: Each chapter includes learning objectives, summaries, and repetition questions with solutions that can help the reader to reassure themselves and strengthen their knowledge. Users who want to familiarise themselves with the field of digital business engineering thus have material at their disposal that is ideal for self-study. But these modules can also help experienced digital business engineers to deepen their knowledge in their organisation and to strengthen their overall methodological competence.
