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Kuniba, Atsuo.

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Quantum groups in three-dimensional integrability

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum groups in three-dimensional integrability/ by Atsuo Kuniba.
Author:	Kuniba, Atsuo.
Published:	Singapore :Springer Nature Singapore : : 2022.,
Description:	xi, 331 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Introduction -- Tetrahedron equation -- 3D R from quantized coordinate ring of type A -- 3D reﬂection equation and quantized reﬂection equation -- 3D K from quantized coordinate ring of type C -- 3D K from quantized coordinate ring of type B -- Intertwiners for quantized coordinate ring Aq (F4) -- Intertwiner for quantized coordinate ring Aq (G2) -- Comments on tetrahedron-type equation for non-crystallographic Coxeter groups -- Connection to PBW bases of nilpotent subalgebra of Uq -- Trace reductions of RLLL = LLLR -- Boundary vector reductions of RLLL = LLLR -- Trace reductions of RRRR = RRRR -- Boundary vector reductions of RRRR = RRRR -- Boundary vector reductions of (LGLG)K = K(GLGL) -- Reductions of quantized G2 reﬂection equation -- Application to multispecies TASEP.
Contained By:	Springer Nature eBook
Subject:	Quantum groups. -
Online resource:	https://doi.org/10.1007/978-981-19-3262-5
ISBN:	9789811932625

Quantum groups in three-dimensional integrability
Kuniba, Atsuo.

Quantum groups in three-dimensional integrability[electronic resource] /by Atsuo Kuniba. - Singapore :Springer Nature Singapore :2022. - xi, 331 p. :ill. (some col.), digital ;24 cm. - Theoretical and mathematical physics,1864-5887. - Theoretical and mathematical physics..

Introduction -- Tetrahedron equation -- 3D R from quantized coordinate ring of type A -- 3D reﬂection equation and quantized reﬂection equation -- 3D K from quantized coordinate ring of type C -- 3D K from quantized coordinate ring of type B -- Intertwiners for quantized coordinate ring Aq (F4) -- Intertwiner for quantized coordinate ring Aq (G2) -- Comments on tetrahedron-type equation for non-crystallographic Coxeter groups -- Connection to PBW bases of nilpotent subalgebra of Uq -- Trace reductions of RLLL = LLLR -- Boundary vector reductions of RLLL = LLLR -- Trace reductions of RRRR = RRRR -- Boundary vector reductions of RRRR = RRRR -- Boundary vector reductions of (LGLG)K = K(GLGL) -- Reductions of quantized G2 reﬂection equation -- Application to multispecies TASEP.

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.

ISBN: 9789811932625

Standard No.: 10.1007/978-981-19-3262-5doiSubjects--Topical Terms:

629837
Quantum groups.

LC Class. No.: QC20.7.G76

Dewey Class. No.: 530.143

Quantum groups in three-dimensional integrability
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100 1 $a Kuniba, Atsuo. $3 3606523
245 1 0 $a Quantum groups in three-dimensional integrability $h [electronic resource] / $c by Atsuo Kuniba.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2022.
300 $a xi, 331 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Theoretical and mathematical physics, $x 1864-5887
505 0 $a Introduction -- Tetrahedron equation -- 3D R from quantized coordinate ring of type A -- 3D reﬂection equation and quantized reﬂection equation -- 3D K from quantized coordinate ring of type C -- 3D K from quantized coordinate ring of type B -- Intertwiners for quantized coordinate ring Aq (F4) -- Intertwiner for quantized coordinate ring Aq (G2) -- Comments on tetrahedron-type equation for non-crystallographic Coxeter groups -- Connection to PBW bases of nilpotent subalgebra of Uq -- Trace reductions of RLLL = LLLR -- Boundary vector reductions of RLLL = LLLR -- Trace reductions of RRRR = RRRR -- Boundary vector reductions of RRRR = RRRR -- Boundary vector reductions of (LGLG)K = K(GLGL) -- Reductions of quantized G2 reﬂection equation -- Application to multispecies TASEP.
520 $a 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.
650 0 $a Quantum groups. $3 629837
650 1 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Quantum Physics. $3 893952
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