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On the structure of some one-generator braces
Part of:
Other nonassociative rings and algebras
Hopf algebras, quantum groups and related topics
Groups and algebras in quantum theory
Published online by Cambridge University Press: 20 March 2024
Abstract
We describe the one-generator braces A satisfying the condition $A^3 = \langle 0 \rangle$.
MSC classification
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
References
Cedó, F., Solutions of the Yang–Baxter Equation, Advances in Group Theory and Applications 5(1) (2018), 33–90.Google Scholar
Cedó, F., Gateva-Ivanova, T. A. and Smoktunowicz, A., On the Yang–Baxter equation and left nilpotent left braces, J. Pure Appl Algebra 221(4) (2017), 751–756.CrossRefGoogle Scholar
Cedó, F., Smoktunowicz, A. and Vendramin, L., Skew left braces of nilpotent type, Proc. London Math. Soc. (3) 118(6) (2019), 1367–1392.CrossRefGoogle Scholar
Jespers, E., van Antwerpen, A. Vendramin, L. Nilpotency of skew braces and multipermutation solution of the Yang–Baxter equation: 2022, preprint, arxiv:2205.01572v1.CrossRefGoogle Scholar
Rump, W., A decomposition theorem for square-free unitary solutions of the quantum Yang–Baxter equation, Adv. Math. 193(1) (2005), 40–55.CrossRefGoogle Scholar
Rump, W., Braces, radical rings, and the quantum Yang–Baxter equation, J. Algebra 307(1) (2007), 153–170.CrossRefGoogle Scholar
Rump, W., Classification of cyclic braces, J. Pure Appl. Algebra 209(3) (2007), 671–685.CrossRefGoogle Scholar
Rump, W., Generalized radical rings, unknotted biquandles, and quantum groups, Colloq. Math. 109(1) (2007), 85–100.CrossRefGoogle Scholar
Rump, W., Semidirect products in algebraic logic and solutions of the quantum Yang–Baxter equation, J. Algebra Appl. 7(4) (2008), 471–490.CrossRefGoogle Scholar
Rump, W., Addendum to “Generalized radical rings, unknotted biquandles, and quantum groups” (Colloq. Math. 109 (2007), 85–100), Colloq. Math. 117(2) (2009), 295–298.CrossRefGoogle Scholar
Smoktunowicz, A., On Engel groups, nilpotent groups, rings, braces and the Yang–Baxter equation, Trans. Amer. Math. Soc. 370(9) (2018), 6535–6564.CrossRefGoogle Scholar