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Distributive biracks and solutions of the Yang–Baxter equation
Authors:
- Přemysl Jedlička,
- Agata Pilitowska,
- Anna Zamojska-Dzienio
Abstract
We investigate a class of non-involutive solutions of the Yang–Baxter equation which generalize derived (self-distributive) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang–Baxter (permutation) groups of such solutions are nilpotent. We formulate the results in the language of biracks which allows us to apply universal algebra tools.
- Record ID
- WUT9d56c66e8d2046a0b7346a71fd10841b
- Author
- Journal series
- International Journal of Algebra and Computation, ISSN 0218-1967, e-ISSN 1793-6500
- Issue year
- 2020
- Vol
- 30
- No
- 03
- Pages
- 667-683
- Publication size in sheets
- 0.80
- Keywords in Polish
- równanie Yanga-Baxtera, rozwiązanie teorio-mnogościowe, rozwiązanie multipermutacyjne, birak, rozdzielność, nilpotentność, kongruencje
- Keywords in English
- Yang-Baxter equation, set-theoretic solution, multipermutation solution, birack, distributivity, nilpotency, congruences
- ASJC Classification
- Abstract in Polish
- Badano nową klasę rozwiązań równania Yanga-Baxtera, która uogólnia rozwiązania pochodne. W szczególności, opisano rozwiązania multipermutacyjne w tej klasie. Grupy permutacji dla tych rozwiązań są nilpotentne. Wyniki uzyskano używając narzędzi algebry uniwersalnej.
- DOI
- DOI:10.1142/S0218196720500150 Opening in a new tab
- URL
- https://www.worldscientific.com/doi/abs/10.1142/S0218196720500150 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 70
- Score source
- journalList
- Score
- = 70.0, 09-05-2022, ArticleFromJournal
- Publication indicators
- = 0; = 3; : 2018 = 0.890; : 2020 (2 years) = 0.719 - 2020 (5 years) =0.632
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- Uniform Resource Identifier
- https://repo.pw.edu.pl/info/article/WUT9d56c66e8d2046a0b7346a71fd10841b/
- URN
urn:pw-repo:WUT9d56c66e8d2046a0b7346a71fd10841b
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.