Title:
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A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras (English) |
Author:
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Chen, Huibin |
Author:
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Deng, Shaoqiang |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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68 |
Issue:
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4 |
Year:
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2018 |
Pages:
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1159-1168 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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left symmetric algebra |
Keyword:
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Novikov superalgebra |
Keyword:
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fermionic Novikov superalgebra |
MSC:
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17A30 |
MSC:
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17A70 |
idZBL:
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Zbl 07031706 |
idMR:
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MR3881905 |
DOI:
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10.21136/CMJ.2018.0144-17 |
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Date available:
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2018-12-07T06:26:24Z |
Last updated:
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2021-01-04 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147530 |
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Reference:
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[1] Bai, C.: Left-symmetric algebras from linear functions.J. Algebra 281 (2004), 651-665. Zbl 1117.17001, MR 2098787, 10.1016/j.jalgebra.2004.06.036 |
Reference:
|
[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. Zbl 0606.58018, MR 0802121 |
Reference:
|
[3] Chen, Z., Ding, M.: A class of Novikov superalgebras.J. Lie Theory 26 (2016), 227-234. Zbl 06589553, MR 3391351 |
Reference:
|
[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. Zbl 0553.35011, MR 0715332 |
Reference:
|
[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. Zbl 0591.58012, MR 0770656 |
Reference:
|
[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. Zbl 0334.58007, MR 0508337, 10.1070/RM1975v030n05ABEH001522 |
Reference:
|
[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. Zbl 0347.49023, MR 0467819, 10.1007/BF01075767 |
Reference:
|
[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. Zbl 0437.58009, MR 0554407, 10.1007/BF01078363 |
Reference:
|
[9] Xu, X.: Hamiltonian operators and associative algebras with a derivation.Lett. Math. Phys. 33 (1995), 1-6. Zbl 0837.16034, MR 1315250, 10.1007/BF00750806 |
Reference:
|
[10] Xu, X.: Hamiltonian superoperators.J. Phys. A, Math. Gen. 28 (1995), 1681-1698. Zbl 0852.58043, MR 1338053, 10.1088/0305-4470/28/6/021 |
Reference:
|
[11] Xu, X.: Variational calculus of supervariables and related algebraic structures.J. Algebra 223 (2000), 396-437. Zbl 1012.37048, MR 1735154, 10.1006/jabr.1999.8064 |
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