Free Delivery Over $100
|
|
|||
|
||||
OverviewChapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups. Full Product DetailsAuthor: L.A. Lambe , D.E. RadfordPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1997 Volume: 423 Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 0.498kg ISBN: 9781461368427ISBN 10: 1461368421 Pages: 300 Publication Date: 23 November 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsForeword. Preface. Introduction. 1. Algebraic Preliminaries. 2. The Quantum Yang-Baxter Equation (QYBE). 3. Categories of Quantum Yang-Baxter Modules. 4. More on the Bialgebra Associated to the QYBE. 5. The Fundamental Example of a Quantum Group. 6. Quasitriangular Structures and the Double. 7. Coquasitriangular Structures. 8. Some Classes of Solutions. 9. Categorical Constructions. Appendices: A-Prerequisites. A.1. The Ground Ring k and Basic k-Linear Maps. A.2. Algebras, Coalgebras, and Their Representations. A.3. Various Notations Related to the QYBE. A.4. Some Results from Linear Algebra. References. Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
