Geodesic
Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 385-392 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find all nonequivalent constant solutions of the classical associative Yang–Baxter equation for $\operatorname{Mat}_3$. New examples found in the classification yield the corresponding Poisson brackets on traces, double Poisson brackets on a free associative algebra with three generators, and anti-Frobenius associative algebras.
Keywords: associative Yang–Baxter equation
Mots-clés : constant solution, classification. 
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V. V. Sokolov. Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 385-392. http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a3/

[1] G.-C. Rota, “Baxter operators, an introduction”, Gian-Carlo Rota on Combinatorics, Contemporary Mathematicians, 57, eds. J. P. S. Kung, Birkhäuser, Boston, MA, 1995, 504–512 | MR

[2] T. Schedler, “Poisson algebras and Yang–Baxter equations”, Advances in Quantum Computation (University of Texas, Tyler, TX, USA, September 20–23, 2007), Contemporary Mathematics, 482, AMS, Providence, RI, 2009, 91–106 | DOI | MR | Zbl

[3] M. Van den Bergh, Trans. Amer. Math. Soc., 360:11 (2008), 5711–5769 | DOI | MR | Zbl

[4] A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, Double Poisson brackets on free associative algebras, Max-Planck-Institut für Mathematik Preprint Series, 52, MPI f. Mathematik, Bonn, 2012, arXiv: 1208.2935 | MR

[5] M. Aguiar, J. Algebra, 244:2 (2001), 492–532 | DOI | MR | Zbl

[6] A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, TMF, 171:1 (2012), 26–32 | DOI | DOI | Zbl

[7] A. V. Mikhailov, V. V. Sokolov, Commun. Math. Phys., 211:1 (2000), 231–251 | DOI | MR | Zbl

[8] C. Procesi, Adv. Math., 19:3 (1976), 306–381 | DOI | MR | Zbl

[9] A. G. Elashvili, Funkts. analiz i ego pril., 16:4 (1982), 94–95 | DOI | MR | Zbl