A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1159-1168 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.
We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.
DOI : 10.21136/CMJ.2018.0144-17
Classification : 17A30, 17A70
Keywords: left symmetric algebra; Novikov superalgebra; fermionic Novikov superalgebra
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Chen, Huibin; Deng, Shaoqiang. A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1159-1168. doi: 10.21136/CMJ.2018.0144-17

[1] Bai, C.: Left-symmetric algebras from linear functions. J. Algebra 281 (2004), 651-665. | DOI | MR | JFM

[2] Balinskii, A. A., Novikov, S. P.: Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras. Sov. Math., Dokl. 32 (1985), 228-231. English. Russian original translation from Dokl. Akad. Nauk SSSR 283 1985 1036-1039. | MR | JFM

[3] Chen, Z., Ding, M.: A class of Novikov superalgebras. J. Lie Theory 26 (2016), 227-234. | MR | JFM

[4] Dubrovin, B. A., Novikov, S. P.: Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov-Whitman averaging method. Sov. Math., Dokl. 27 (1983), 665-669. English. Russian original translation from Dokl. Akad. Nauk SSSR 270 1983 781-785. | MR | JFM

[5] Dubrovin, B. A., Novikov, S. P.: On Poisson brackets of hydrodynamic type. Sov. Math., Dokl. 30 (1984), 651-654. English. Russian original translation from Dokl. Akad. Nauk SSSR 279 1984 294-297. | MR | JFM

[6] Gel'fand, I. M., Dikii, L. A.: Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg-de Vries equations. Russ. Math. Surv. 30 (1975), 77-113. English. Russian original translation from Usp. Mat. Nauk\kern0pt 30 1975 67-100. | DOI | MR | JFM

[7] Gel'fand, I. M., Dikii, L. A.: A Lie algebra structure in a formal variational calculation. Funct. Anal. Appl. 10 (1976), 16-22. English. Russian original translation from Funkts. Anal. Prilozh. 10 1976 18-25. | DOI | MR | JFM

[8] Gel'fand, I. M., Dorfman, I. Ya.: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Appl. 13 (1980), 248-262. English. Russian original translation from Funkts. Anal. Prilozh. 13 1980 13-30. | DOI | MR | JFM

[9] Xu, X.: Hamiltonian operators and associative algebras with a derivation. Lett. Math. Phys. 33 (1995), 1-6. | DOI | MR | JFM

[10] Xu, X.: Hamiltonian superoperators. J. Phys. A, Math. Gen. 28 (1995), 1681-1698. | DOI | MR | JFM

[11] Xu, X.: Variational calculus of supervariables and related algebraic structures. J. Algebra 223 (2000), 396-437. | DOI | MR | JFM

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