Quantum Groups in Three-Dimensional Integrability / Theoretical and Mathematical Physics (PDF)
(Sprache: Englisch)
Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups,...
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Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac-Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions.
This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation, and its solution due to work byKapranov-Voevodsky (1994).
Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré-Birkhoff-Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang-Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc.
These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.
Bibliographische Angaben
- Autor: Atsuo Kuniba
- 2022, 1st ed. 2022, 331 Seiten, Englisch
- Verlag: Springer Nature Singapore
- ISBN-10: 981193262X
- ISBN-13: 9789811932625
- Erscheinungsdatum: 25.09.2022
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
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