A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras

Huibin Chen; Shaoqiang Deng

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 1159-1168
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Chen, Huibin, and Deng, Shaoqiang. "A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras." Czechoslovak Mathematical Journal 68.4 (2018): 1159-1168. <http://eudml.org/doc/294267>.

@article{Chen2018,
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.},
author = {Chen, Huibin, Deng, Shaoqiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {left symmetric algebra; Novikov superalgebra; fermionic Novikov superalgebra},
language = {eng},
number = {4},
pages = {1159-1168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras},
url = {http://eudml.org/doc/294267},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Chen, Huibin
AU - Deng, Shaoqiang
TI - A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1159
EP - 1168
AB - 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.
LA - eng
KW - left symmetric algebra; Novikov superalgebra; fermionic Novikov superalgebra
UR - http://eudml.org/doc/294267
ER -

References

top
  1. Bai, C., 10.1016/j.jalgebra.2004.06.036, J. Algebra 281 (2004), 651-665. (2004) Zbl1117.17001MR2098787DOI10.1016/j.jalgebra.2004.06.036
  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. (1985) Zbl0606.58018MR0802121
  3. Chen, Z., Ding, M., A class of Novikov superalgebras, J. Lie Theory 26 (2016), 227-234. (2016) Zbl06589553MR3391351
  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. (1983) Zbl0553.35011MR0715332
  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. (1984) Zbl0591.58012MR0770656
  6. Gel'fand, I. M., Dikii, L. A., 10.1070/RM1975v030n05ABEH001522, Russ. Math. Surv. 30 (1975), 77-113. English. Russian original translation from Usp. Mat. Nauk30 1975 67-100. (1975) Zbl0334.58007MR0508337DOI10.1070/RM1975v030n05ABEH001522
  7. Gel'fand, I. M., Dikii, L. A., 10.1007/BF01075767, Funct. Anal. Appl. 10 (1976), 16-22. English. Russian original translation from Funkts. Anal. Prilozh. 10 1976 18-25. (1976) Zbl0347.49023MR0467819DOI10.1007/BF01075767
  8. Gel'fand, I. M., Dorfman, I. Ya., 10.1007/BF01078363, Funct. Anal. Appl. 13 (1980), 248-262. English. Russian original translation from Funkts. Anal. Prilozh. 13 1980 13-30. (1980) Zbl0437.58009MR0554407DOI10.1007/BF01078363
  9. Xu, X., 10.1007/BF00750806, Lett. Math. Phys. 33 (1995), 1-6. (1995) Zbl0837.16034MR1315250DOI10.1007/BF00750806
  10. Xu, X., 10.1088/0305-4470/28/6/021, J. Phys. A, Math. Gen. 28 (1995), 1681-1698. (1995) Zbl0852.58043MR1338053DOI10.1088/0305-4470/28/6/021
  11. Xu, X., 10.1006/jabr.1999.8064, J. Algebra 223 (2000), 396-437. (2000) Zbl1012.37048MR1735154DOI10.1006/jabr.1999.8064

NotesEmbed ?

top

You must be logged in to post comments.