Abstract
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.
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References
C. Bai: Left-symmetric algebras from linear functions. J. Algebra 281 (2004), 651–665.
A. A. Balinskii, S. P. Novikov: Poisson brackets of hydrodynamic type, Frobenius al-gebras and Lie algebras. Sov. Math., Dokl. 32 (1985), 228–231. (In English. Russian original.); translation from Dokl. Akad. Nauk SSSR 283 (1985), 1036–1039.
Z. Chen, M. Ding: A class of Novikov superalgebras. J. Lie Theory 26 (2016), 227–234.
B. A. Dubrovin, S. P. Novikov: Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov-Whitman averaging method. Sov. Math., Dokl. 27 (1983), 665–669. (In English. Russian original.); translation from Dokl. Akad. Nauk SSSR 270 (1983), 781–785.
B. A. Dubrovin, S. P. Novikov: On Poisson brackets of hydrodynamic type. Sov. Math., Dokl. 30 (1984), 651–654. (In English. Russian original.); translation from Dokl. Akad. Nauk SSSR 279 (1984), 294–297.
I. M. Gel’fand, L. A. Dikii: 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. (In English. Russian original.); translation from Usp. Mat. Nauk 30 (1975), 67–100.
I. M. Gel’fand, L. A. Dikii: A Lie algebra structure in a formal variational calculation. Funct. Anal. Appl. 10 (1976), 16–22. (In English. Russian original.); translation from Funkts. Anal. Prilozh. 10 (1976), 18–25.
I. M. Gel’fand, I. Ya. Dorfman: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Appl. 13 (1980), 248–262. (In English. Russian original.); trans-lation from Funkts. Anal. Prilozh. 13 (1980), 13–30.
X. Xu: Hamiltonian operators and associative algebras with a derivation. Lett. Math. Phys. 33 (1995), 1–6.
X. Xu: Hamiltonian superoperators. J. Phys. A, Math. Gen. 28 (1995), 1681–1698.
X. Xu: Variational calculus of supervariables and related algebraic structures. J. Algebra 223 (2000), 396–437.
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The research has been supported by NSFC (no. 11671212, 51535008).
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Chen, H., Deng, S. A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras. Czech Math J 68, 1159–1168 (2018). https://doi.org/10.21136/CMJ.2018.0144-17
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DOI: https://doi.org/10.21136/CMJ.2018.0144-17