More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. "Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. Ludwig,Sam NelsonĬLICK HERE TO GET BOOK Book Encyclopedia of Knot Theory Description/Summary: Publisher : Springer Science & Business MediaĪuthor : Colin Adams,Erica Flapan,Allison Henrich,Louis H. 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. We note the quantized enveloping algebras described Hopf algebras. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. For this reason we develop their theory in some detail. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. 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. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. The material here not specifically cited can be found for the most part in in one form or another, with a few exceptions. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. This chapter should be used as reference material and should be consulted as needed. CLICK HERE TO GET BOOK Book Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach Description/Summary:Ĭhapter 1 The algebraic prerequisites for the book are covered here and in the appendix.