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Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation.(English)Zbl 1412.16023

Summary: We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.

MSC:

16T25 Yang-Baxter equations
20E22 Extensions, wreath products, and other compositions of groups
20F16 Solvable groups, supersolvable groups

Cite

References:

[1]Andruskiewitsch, N.; Graña, M., From racks to pointed Hopf algebras, Adv. Math., 178, 2, 177-243 (2003) ·Zbl 1032.16028
[2]Bachiller, D.; Cedó, F.; Jespers, E.; Okniński, J., A family of irretractable square-free solutions of the Yang-Baxter equation, Forum Math., 29, 6, 1291-1306 (2017) ·Zbl 1394.16041
[3]Bachiller, F.; Cedó, D.; Vendramin, L., A characterization of finite multipermutation solutions of the Yang-Baxter equation, Publ. Mat., 62, 641-649 (2018) ·Zbl 1432.16030
[4]Castelli, M.; Catino, F.; Pinto, G., A new family of set-theoretic solutions of the Yang-Baxter equation, Commun. Algebra, 46, 4, 1622-1629 (2017) ·Zbl 1440.16038
[5]Chouraqui, F., Garside groups and Yang-Baxter equation, Commun. Algebra, 38, 12, 4441-4460 (2010) ·Zbl 1216.16023
[6]Chouraqui, F., Left orders in Garside groups, Int. J. Algebra Comput., 26, 07, 1349-1359 (2016) ·Zbl 1357.20015
[7]Chouraqui, F.; Godelle, E., Folding of set-theoretical solutions of the Yang-Baxter equation, Algebr. Represent. Theory, 15, 1277-1290 (2012) ·Zbl 1264.16038
[8]Drinfeld, V. G., On some unsolved problems in quantum group theory, (Quantum Groups. Quantum Groups, Leningrad, 1990. Quantum Groups. Quantum Groups, Leningrad, 1990, Lect. Notes Math., vol. 1510 (1992), Springer-Verlag: Springer-Verlag Berlin), 1-8 ·Zbl 0765.17014
[9]Etingof, P.; Schedler, T.; Soloviev, A., Set-theoretical solutions to the Quantum Yang-Baxter equation, Duke Math. J., 100, 2, 169-209 (1999) ·Zbl 0969.81030
[10]Gateva-Ivanova, T., A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation, J. Math. Phys., 45, 10, 3828-3858 (2004) ·Zbl 1065.16037
[11]Gateva-Ivanova, T.; Van den Bergh, M., Semigroups of I-Type, J. Algebra, 206, 1, 97-112 (1998) ·Zbl 0944.20049
[12]Godelle, E., Parabolic subgroups of Garside groups, J. Algebra, 317, 1, 1-16 (2007) ·Zbl 1173.20027
[13]Jespers, E.; Okniński, J., Monoids and groups of I-type, Algebr. Represent. Theory, 8, 5, 709-729 (2005) ·Zbl 1091.20024
[14]Jespers, E.; Okniński, J., Noetherian Semigroup Algebras (2007), Springer-Verlag: Springer-Verlag Dordrecht ·Zbl 1178.16025
[15]Lebed, V.; Vendramin, L., Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation, Adv. Math., 304, 1219-1261 (2017) ·Zbl 1356.16027
[16]Passman, D. S., The Algebraic Structure of Group Rings (1977), Wiley-Interscience: Wiley-Interscience New York ·Zbl 0368.16003
[17]Promislow, S. D., A simple example of a torsion-free, non unique product group, Bull. Lond. Math. Soc., 20, 4, 302-304 (1988) ·Zbl 0662.20022
[18]Robinson, D. J., A Course in the Theory of Groups, vol. 80 (1996), Springer-Verlag: Springer-Verlag New York
[19]Rump, W., A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation, Adv. Math., 193, 40-55 (2005) ·Zbl 1074.81036
[20]Rump, W., Semidirect products in algebraic logic and solutions of the quantum Yang-Baxter equation, J. Algebra Appl., 7, 04, 471-490 (2008) ·Zbl 1153.81505
[21]Smoktunowicz, A.; Smoktunowicz, A., Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices, Linear Algebra Appl., 546, 86-114 (2018) ·Zbl 1384.16025
[22]Strojnowski, A., A note on up groups, Commun. Algebra, 8, 3, 231-234 (1980) ·Zbl 0423.20005
[23]Vendramin, L., Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova, J. Pure Appl. Algebra, 220, 2064-2076 (2016) ·Zbl 1337.16028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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