Yang–Baxter maps, discrete integrable equations and quantum groups
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Bazhanov, Vladimir V.; Sergeev, Sergey M.
Description
For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang–Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of...[Show more]
dc.contributor.author | Bazhanov, Vladimir V. | |
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dc.contributor.author | Sergeev, Sergey M. | |
dc.date.accessioned | 2018-01-10T04:09:12Z | |
dc.date.available | 2018-01-10T04:09:12Z | |
dc.identifier.issn | 0550-3213 | |
dc.identifier.uri | http://hdl.handle.net/1885/139155 | |
dc.description.abstract | For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang–Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang–Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq(sl(2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra. | |
dc.format.mimetype | application/pdf | |
dc.publisher | Elsevier | |
dc.rights | © 2017 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 | |
dc.source | Nuclear Physics B | |
dc.title | Yang–Baxter maps, discrete integrable equations and quantum groups | |
dc.type | Journal article | |
local.identifier.citationvolume | 926 | |
dc.date.issued | 2018 | |
local.publisher.url | https://www.elsevier.com/ | |
local.type.status | Published Version | |
local.contributor.affiliation | Bazhanov, V. V., Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University | |
local.contributor.affiliation | Sergeev, S. M., Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University | |
local.bibliographicCitation.startpage | 509 | |
local.bibliographicCitation.lastpage | 543 | |
local.identifier.doi | 10.1016/j.nuclphysb.2017.11.017 | |
dcterms.accessRights | Open Access | |
Collections | ANU Research Publications |
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