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On Hom-Jordan algebras and their \(\alpha ^{k}-(a,b,c)\) type derivations

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Abstract

In this paper we generalize the results in Huang et al. (Commun Algebra 46:2600–2614, 2018). 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.

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References

  • Albert, A.: A structure theory for Jordan algebras. Ann. Math. 48(2), 546–567 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  • Argaç, N., Alba, S.E.: On generalized \( (\sigma , \tau )\)-derivations. Sib. Math. J. 43(6), 977–984 (2002)

    Article  Google Scholar 

  • Argaç, N., Inceboz, H.: On generalized \( (\sigma, \tau ) \)-derivations II. J. Korean Math. Soc. 47(3), 495–504 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Benayadi, S., Makhlouf, A.: Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. J. Geom. Phys. 76(2), 38–60 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, N., Chen, L., Wang, Y.: Hom-Jordan algebras and their \(\alpha ^{k}-(a, b, c)\)-derivations. Commun. Algebra 46(6), 2600–2614 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Kaigorodov, I.: On \( \delta \)-derivations of classical Lie superalgebras. Sib. Math. J. 50(3), 434–449 (2009)

    Article  MathSciNet  Google Scholar 

  • Leger, G.F., Luks, E.M.: Generalized derivations of lie algebras. J. Algebra 228, 165–203 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Li, M.: Quasicentroid of Lie superalgebra, Master Degree thesis, Harbin Normal University (in Chinese) (2011)

  • Makhlouf, A.: Hom-alternative algebras and Hom-Jordan algebras. Int. Electron. J. Algebra 8, 177–190 (2010)

    MathSciNet  MATH  Google Scholar 

  • Meng, D.: Abstract algebra II, associative algebra, pp. 152–157. Science Press, Beijing (2011).. (in Chinese)

    Google Scholar 

  • Yao, C., Yao, M., Liangyun, C.: Generalized derivations of Hom–Jordan algebras. arXiv:1906.04551 (2019)

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Authors and Affiliations

  1. Department of Mathematics, Physics and Computer Science, LSI, University Sidi Mohammed Ben Abdellah, Polydisciplinary Faculty, Taza, Morocco

    Abdelkarim Boua

  2. Department of Mathematics, Fayoum University, Faculty of Science, Fayoum, Egypt

    Mahmoud M. El-Soufi

  3. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Ahmed Y. Abdelwanis

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  1. Abdelkarim Boua
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  2. Mahmoud M. El-Soufi
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  3. Ahmed Y. Abdelwanis
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Boua, A., El-Soufi, M.M. & Abdelwanis, A.Y. On Hom-Jordan algebras and their \(\alpha ^{k}-(a,b,c)\) type derivations. Beitr Algebra Geom 64, 267–284 (2023). https://doi.org/10.1007/s13366-022-00632-4

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  • DOI: https://doi.org/10.1007/s13366-022-00632-4

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