Quantum Groups in Three-Dimensional Integrability / Theoretical and Mathematical Physics (PDF)

Name: Quantum Groups in Three-Dimensional Integrability / Theoretical and Mathematical Physics
Brand: Springer Nature Singapore
SKU: 145218219
Price: 98.99 EUR
Availability: OnlineOnly

(Sprache: Englisch)

Autor: Atsuo Kuniba

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Quantum Groups in Three-Dimensional Integrability / Theoretical and Mathematical Physics, Atsuo Kuniba

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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 U_q and A_q. 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 U_q, 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 A_q. 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 U_q, 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.