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CC-BY-NC - Uznanie autorstwa - Użycie niekomercyjneFinite Idempotent Set-Theoretic Solutions of the Yang–Baxter Equation
| dc.abstract.en | It is proven that finite idempotent left non-degenerate set-theoretic solutions (X,r) of the Yang–Baxter equation on a set X are determined by a left simple semigroup structure on X (in particular, a finite union of isomorphic copies of a group) and some maps q and φx on X, for x∈X. This structure turns out to be a group precisely when the associated Yang–Baxter monoid M(X,r) is cancellative and all the maps φx are equal to an automorphism of this group. Equivalently, the Yang–Baxter algebra K[M(X,r)] is right Noetherian, or in characteristic zero it has to be semiprime. The Yang–Baxter algebra is always a left Noetherian representable algebra of Gelfand–Kirillov dimension one. To prove these results, it is shown that the Yang–Baxter semigroup S(X,r) has a decomposition in finitely many cancellative semigroups Su indexed by the diagonal, each Su has a group of quotients Gu that is finite-by-(infinite cyclic) and the union of these groups carries the structure of a left simple semigroup. The case that X equals the diagonal is fully described by a single permutation on X. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Kubat, Łukasz |
| dc.contributor.author | Verwimp, Charlotte |
| dc.contributor.author | Antwerpen, Arne Van |
| dc.contributor.author | Jespers, Eric |
| dc.contributor.author | Colazzo, Ilaria |
| dc.date.accessioned | 2024-01-25T00:41:09Z |
| dc.date.available | 2024-01-25T00:41:09Z |
| dc.date.copyright | 2023-08-15 |
| dc.date.issued | 2023 |
| dc.description.accesstime | AT_PUBLICATION |
| dc.description.finance | Publikacja bezkosztowa |
| dc.description.version | FINAL_PUBLISHED |
| dc.identifier.doi | 10.1093/IMRN/RNAD183 |
| dc.identifier.issn | 1073-7928 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/107176 |
| dc.identifier.weblink | https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad183/51112327/rnad183.pdf |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | International Mathematics Research Notices |
| dc.relation.pages | 1-32 |
| dc.rights | CC-BY-NC |
| dc.sciencecloud | nosend |
| dc.title | Finite Idempotent Set-Theoretic Solutions of the Yang–Baxter Equation |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |