Novikov--Poisson anlgebras in low dimension
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 381-393.

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We classify Novikov–Poisson algebras in low dimmension. Also we obtain examples of the Novikov–Poisson algebra of non vector type.
Mots-clés : Novikov–Poisson algebra, nonassociative algebras.
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A. S. Zakharov. Novikov--Poisson anlgebras in low dimension. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 381-393. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a16/

[1] Xu X., “Novikov–Poisson algebra”, J. Algebra, 190:2 (1997), 253–279 | DOI | MR | Zbl

[2] I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and algebraic structures related to them”, Funktsional. Anal. i Prilozhen., 13:4 (1979), 13–30 | MR | Zbl

[3] A. A. Balinskii, S. P. Novikov, “Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras”, Dokl. Akad. Nauk SSSR, 283:5 (1985), 1036–1039 | MR | Zbl

[4] E. I. Zelmanov, “A class of local translation-invariant Lie algebras”, Dokl. Akad. Nauk SSSR, 292:6 (1987), 1294–1297 | MR | Zbl

[5] V. T. Filippov, “A class of simple nonassociative algebras”, Mat. Zametki, 45:1 (1989), 101–105 | MR

[6] J. M. Osborn, “Modules for Novikov algebras”, Contemp. Math., 184, 1991, 327–338 | MR

[7] J. M. Osborn, “Novikov algebras”, Nova J. Algebra Geom., 1:1 (1992), 1–13 | MR | Zbl

[8] J. M. Osborn, “Simple Novikov algebra with an idempotent”, Commun. Algebra, 20:9 (1992), 2729–2753 | DOI | MR | Zbl

[9] X. Xu, “On Simple Novikov Algebras and Their Irreducible Modules”, J. Algebra, 185 (1996), 905–934 | DOI | MR | Zbl

[10] Xu X., “Classification of simple Novikov Algebra and their irreducible modules of characterestic 0”, J. Algebra, 246:2 (2001), 673–707 | DOI | MR | Zbl

[11] V. N. Zhelyabin, A. S. Tikhov, “Algebry Novikova–Puassona i assotsiativnye kommutativnye differentsialnye algebry”, Algebra i logika, 47:2 (2008), 186–202 | MR | Zbl

[12] A. S. Zakharov, “Novikov–Poisson algebras and superalgebras of Jordan brackets”, Commun. Algebra, 42:5 (2014), 2285–2298 | DOI | MR | Zbl

[13] A. S. Zakharov, “Vlozhenie algebr Novikova–Puassona v algebry Novikova–Puassona vektornogo tipa”, Algebra i logika, 52:3 (2013), 352–369 | MR | Zbl

[14] V. N. Zhelyabin, A. S. Zakharov, “Spetsialnost iordanovykh superalgebr, svyazannykh s algebrami Novikova–Puassona”, Mat. zametki, 97:3 (2015), 359–367 | DOI

[15] C. Bai, D. Meng, “The classification of Novikov algebras in low dimensions”, J. Phys. A: Math. Gen., 34 (2001), 1581–1594 | DOI | MR | Zbl