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Quantum Groups in Three-Dimensional Integrability by Atsuo Kuniba is a nonfiction available to read on EtoBox.

What is Quantum Groups in Three-Dimensional Integrability about?

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,  G 2 reflection equation

Who reads Quantum Groups in Three-Dimensional Integrability?

Author

Atsuo Kuniba

Publisher

Springer Nature Singapore Pte Ltd Fka Springer Science + Business Media Singapore Pte Ltd

Published

2022

Language

EN

ISBN

9789811932625

Category

nonfiction

Subjects

Science, Physics, Stem