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Quantum Groups in Three-Dimensional Integrability

Quantum Groups in Three-Dimensional Integrability


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About the Book

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 by Kapranov-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.


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Product Details
  • ISBN-13: 9789811932618
  • Publisher: Springer Nature Singapore
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Weight: 707 gr
  • ISBN-10: 9811932611
  • Publisher Date: 26 Sep 2022
  • Height: 234 mm
  • No of Pages: 331
  • Spine Width: 21 mm
  • Width: 156 mm


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Quantum Groups in Three-Dimensional Integrability
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