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Quantum Groups in Three-Dimensional Integrability
Af: Atsuo Kuniba
Engelsk
Bogcover for Quantum Groups in Three-Dimensional Integrability af Atsuo Kuniba, 9789811932618
Specifikationer
Sprog:
Engelsk
Sider:
331
ISBN-13:
9789811932618
Indbinding:
Hardback
ISBN-10:
9811932611
Kategori:
Udg. Dato:
26 sep 2022
Størrelse i cm:
23,5 x 15,5
Forlag:
Oplagsdato:
26 sep 2022
Forfatter(e):
Genre:

Quantum Groups in Three-Dimensional Integrability

Af: Atsuo Kuniba
Engelsk
Format:
Bog beskrivelse
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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Specifikationer
Sprog:
Engelsk
Sider:
331
ISBN-13:
9789811932618
Indbinding:
Hardback
ISBN-10:
9811932611
Kategori:
Udg. Dato:
26 sep 2022
Størrelse i cm:
23,5 x 15,5
Forlag:
Oplagsdato:
26 sep 2022
Forfatter(e):
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