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Quantum Groups in Three-Dimensional Integrability
Af: Atsuo Kuniba Engelsk Hardback
SPAR
kr 253
Quantum Groups in Three-Dimensional Integrability
Af: Atsuo Kuniba Engelsk Hardback
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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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.


Produktdetaljer
Sprog: Engelsk
Sider: 331
ISBN-13: 9789811932618
Indbinding: Hardback
Udgave:
ISBN-10: 9811932611
Udg. Dato: 26 sep 2022
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 26 sep 2022
Forfatter(e): Atsuo Kuniba
Forfatter(e) Atsuo Kuniba


Kategori Kvantefysik, kvantemekanik og kvantefeltteori


Sprog Engelsk


Indbinding Hardback


Sider 331


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 26 sep 2022


Oplagsdato 26 sep 2022

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