Quantum groups in three-dimensional integrability
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…
Read More ↓Title Statements
- Full title :Quantum groups in three-dimensional integrability / Atsuo Kuniba.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2022
Publication Statements
- Publisher(s):Springer Nature Singapore
- Place of Publication:Singapore
- Language:eng
- Publication Date:2022
The Physical Object
- Description:xi, 331 Seiten : Illustrationen
Edition Identifiers
- ISBN:9789811932618, 9811932611, 9789811932632, 9811932638
- DOI:10.1007/978-981-19-3262-5
- oclc:on1349644761
- Dewey Decimal:530.15
Subjects
Writers
No reviews yet. Be the first to rate this work.
Related Works
more →
Nonstandard analysis and its applications
Spacetime without reference frames
Variational methods in nonlinear field equations: solitary waves, hylomorphic solitons an…
Benci, V., (Vieri)
Quantum field theory for mathematicians
Noncommutative geometry and physics 4
Files & Downloads
-
Quantum Groups in Three-Dimensional Integrability…
PDF · 5.7 MB · updated -
Quantum Groups in Three-Dimensional Integrability…
PDF · 5.6 MB · updated
Rate & Review