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Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach - L.A. Lambe, D.E. Radford

Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach

Buch | Hardcover
300 Seiten
1997
Springer (Verlag)
978-0-7923-4721-7 (ISBN)
CHF 74,85 inkl. MwSt
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 class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras.
Chapter 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.

Foreword. 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.

Erscheint lt. Verlag 31.10.1997
Reihe/Serie Mathematics and Its Applications ; 423
Mathematics and Its Applications ; 423
Zusatzinfo XX, 300 p.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie
ISBN-10 0-7923-4721-8 / 0792347218
ISBN-13 978-0-7923-4721-7 / 9780792347217
Zustand Neuware
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