Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2021_18_2_a2, author = {V. Gubarev}, title = {An example of a simple double {Lie} algebra}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {834--844}, publisher = {mathdoc}, volume = {18}, number = {2}, year = {2021}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a2/} }
V. Gubarev. An example of a simple double Lie algebra. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 834-844. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a2/
[1] M. Van den Bergh, “Double Poisson algebras”, Trans. Am. Math. Soc., 360:11 (2008), 5711–5769 | DOI | Zbl
[2] W. Crawley-Boevey, “Poisson structures on moduli spaces of representations”, J. Algebra, 325:1 (2011), 205–215 | DOI | Zbl
[3] N. Iyudu, M. Kontsevich, Y. Vlassopoulos, “Pre-Calabi-Yau algebras as noncommutative Poisson structures”, J. Algebra, 567 (2021), 63–90 | DOI | Zbl
[4] A. De Sole, V.G. Kac, D. Valeri, “Double Poisson vertex algebras and non-commutative Hamiltonian equations”, Adv. Math., 281 (2015), 1025–1099 | DOI | Zbl
[5] A. Odesskii, V. Rubtsov, V. Sokolov, “Double Poisson brackets on free associative algebras”, Noncommutative birational geometry, representations and combinatorics, Contemp. Math., 592, eds. Berenstein A. et al., 2013, 225–239 | DOI | Zbl
[6] M.E. Goncharov, P.S. Kolesnikov, “Simple finite-dimensional double algebras”, J. Algebra, 500 (2018), 425–438 | DOI | Zbl
[7] T. Schedler, “Poisson algebras and Yang-Baxter equations”, Contemp. Math., 482, eds. Mahdavi Kazem et al., 2009, 91–106 | DOI | Zbl
[8] F.G. Tricomi, “On the finite Hilbert transformation”, Q. J. Math., Oxf. II. Ser., 2 (1951), 199–211 | DOI | Zbl
[9] G. Baxter, “An analytic problem whose solution follows from a simple algebraic identity”, Pac. J. Math., 10 (1960), 731–742 | DOI | Zbl
[10] A.A. Belavin, V.G. Drinfel'd, “Solutions of the classical Yang-Baxter equation for simple Lie algebras”, Funct. Anal. Appl., 16 (1983), 159–180 | DOI | Zbl
[11] L. Guo, An introduction to Rota-Baxter algebra, Surveys of Modern Mathematics, 4, International Press, Somerville; Higher education press, Beijing, 2012 | Zbl
[12] M. Aguiar, “Pre-Poisson algebras”, Lett. Math. Phys., 54:4 (2000), 263–277 | DOI | Zbl
[13] V. Gubarev, “Rota-Baxter operators on unital algebras”, Mosc. Math. J., 21:2 (2021), 325–364 | DOI | Zbl
[14] V.N. Zhelyabin, “Jordan bialgebras of symmetric elements and Lie bialgebras”, Sib. Math. J., 39:2 (1998), 261–276 | DOI | Zbl
[15] M. Aguiar, “On the associative analog of Lie bialgebras”, J. Algebra, 244:2 (2001), 492–532 | DOI | Zbl
[16] A. Polishchuk, “Classical Yang-Baxter equation and the $A_\infty$-constraint”, Adv. Math., 168:1 (2002), 56–95 | DOI | Zbl
[17] B.A. Kupershmidt, “What a classical $r$-matrix really is”, J. Nonlinear Math. Phys., 6:4 (1999), 448–488 | DOI | Zbl
[18] K. Uchino, “Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators”, Lett. Math. Phys., 85:2–3 (2008), 91–109 | DOI | Zbl
[19] A. Pichereau, G. Van den Weyer, “Double Poisson cohomology of path algebras of quivers”, J. Algebra, 319:5 (2008), 2166–2208 | DOI | Zbl
[20] M. Aguiar, “Infinitesimal Hopf algebras”, Contemp. Math., 267, 2000, 1–29 | DOI | Zbl
[21] V.V. Sokolov, “Classification of constant solutions of the associative Yang-Baxter equation on $\mathrm{Mat}_3$”, Theor. Math. Phys., 176:3 (2013), 1156–1162 | DOI | Zbl
[22] S.G. Kolesnikov, N.V. Mal'tsev, “Derivations of matrix rings containing a subring of triangular matrices”, Russ. Math., 55:11 (2011), 18–26 | DOI | Zbl