On Hom-Jordan algebras and their \(\alpha^k -(a,b,c)\) type derivations. (English) Zbl 1520.17036
Beitr. Algebra Geom. 64, No. 2, 267-284 (2023); correction ibid. 64, No. 2, 285 (2023).
Summary: In this paper we generalize the results in [N. Huang et al., Commun. Algebra 46, No. 6, 2600–2614 (2018; Zbl 1443.17010)]. The current paper studies \(\alpha^k -(a, b, c)\)-type derivations of Hom-Jordan algebras. First, we give some properties of Hom-Jordan algebra and homomorphisms of Hom-Jordan algebras. Second, we get on some properties of \(\alpha^k\)-centroids and \(\alpha^k\)-quasicentroids of Hom-Jordan algebras. Finally, we study quasiderivations and \(\alpha^k -(a, b, c)\)-quasiderivations of Hom-Jordan algebras.
Keywords:
\(\alpha^k -(a, b, c)\)-quasiderivations; generalized \(\alpha^k -(a, b, c)\)-derivations; Hom-Jordan algebrasCitations:
Zbl 1443.17010References:
| [1] | Albert, A., A structure theory for Jordan algebras, Ann. Math., 48, 2, 546-567 (1947) · Zbl 0029.01003 · doi:10.2307/1969128 |
| [2] | Argaç, N.; Alba, SE, On generalized \((\sigma , \tau )\)-derivations, Sib. Math. J., 43, 6, 977-984 (2002) · Zbl 1016.16023 · doi:10.1023/A:1021172031215 |
| [3] | Argaç, N.; Inceboz, H., On generalized \((\sigma, \tau ) \)-derivations II, J. Korean Math. Soc., 47, 3, 495-504 (2010) · Zbl 1191.16039 · doi:10.4134/JKMS.2010.47.3.495 |
| [4] | Benayadi, S.; Makhlouf, A., Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys., 76, 2, 38-60 (2014) · Zbl 1331.17028 · doi:10.1016/j.geomphys.2013.10.010 |
| [5] | Huang, N.; Chen, L.; Wang, Y., Hom-Jordan algebras and their \(\alpha^k-(a, b, c)\)-derivations, Commun. Algebra, 46, 6, 2600-2614 (2018) · Zbl 1443.17010 · doi:10.1080/00927872.2017.1392535 |
| [6] | Kaigorodov, I., On \(\delta \)-derivations of classical Lie superalgebras, Sib. Math. J., 50, 3, 434-449 (2009) · Zbl 1221.17019 · doi:10.1007/s11202-009-0049-9 |
| [7] | Leger, GF; Luks, EM, Generalized derivations of lie algebras, J. Algebra, 228, 165-203 (2000) · Zbl 0961.17010 · doi:10.1006/jabr.1999.8250 |
| [8] | Li, M.: Quasicentroid of Lie superalgebra, Master Degree thesis, Harbin Normal University (in Chinese) (2011) |
| [9] | Makhlouf, A., Hom-alternative algebras and Hom-Jordan algebras, Int. Electron. J. Algebra, 8, 177-190 (2010) · Zbl 1335.17018 |
| [10] | Meng, D., Abstract algebra II, associative algebra, 152-157 (2011), Beijing: Science Press, Beijing |
| [11] | Yao, C., Yao, M., Liangyun, C.: Generalized derivations of Hom-Jordan algebras. arXiv:1906.04551 (2019) · Zbl 1531.17023 |
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