Idempotent solutions of the Yang-Baxter equation and twisted group division
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436393" target="_blank" >RIV/00216208:11320/21:10436393 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=3SPoGn_ld3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=3SPoGn_ld3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/fm872-2-2021" target="_blank" >10.4064/fm872-2-2021</a>
Alternative languages
Result language
angličtina
Original language name
Idempotent solutions of the Yang-Baxter equation and twisted group division
Original language description
Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the identity (x * y) * (x * z) = (y * y) * (y * z). Using combinatorial properties of the Cayley kernel and the squaring mapping, we prove that a twisted Ward left quasigroup of prime order is either permutational or a quasigroup. Up to isomorphism, all twisted Ward quasigroups (X, *) are obtained by twisting the left division operation in groups (that is, they are of the form x * y = (sic)(x(-1) y) for a group (X, .) and its automorphism (sic)), and they correspond to idempotent Latin solutions. We solve the isomorphism problem for idempotent Latin solutions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fundamenta Mathematicae
ISSN
0016-2736
e-ISSN
—
Volume of the periodical
2021
Issue of the periodical within the volume
255
Country of publishing house
PL - POLAND
Number of pages
18
Pages from-to
51-68
UT code for WoS article
000675601800003
EID of the result in the Scopus database
2-s2.0-85111113971