Almost inner derivations of Leibniz algebras

Year 2024, Volume: 73 Issue: 4, 969 - 981, 30.12.2024

Nil Mansuroğlu , Mücahit Özkaya

https://doi.org/10.31801/cfsuasmas.1485446

https://izlik.org/JA38LY42NM

Abstract

This work is presented the study on almost inner derivations of Leibniz algebras. In this note, we demonstrate the natural extensions of some general properties on derivations given for Lie algebras to Leibniz algebras with finite dimension, and also we investigate which statements a mapping have to hold to be an almost inner derivation.

Keywords

Leibniz algebra , derivation , almost inner derivation

References

• Bloh, A. M., A generalization of the concept of Lie algebras, Doklady Akademii Nauk, 165 (1965), 471-473.
• Bloh, A. M., A certain generalization of the concept of Lie algebras, Algebra and Number Theory Moskow. Gos. Ped. Inst Ucen, 375 (1971), 9-20.
• Burde, D., Dekimpe, K., Verbeke, B., Almost inner derivations of Lie algebras, Journal of Algebra and Its Applications, 17(11) (2018). https://doi.org/10.1142/S0219498818502146
• Centrone, L., Yasumura, F., Actions of Taft’s algebras on finite dimensional algebras, Journal of Algebra, 560 (2020), 725-744. https://doi.org/10.1016/j.jalgebra.2020.06.007
• Centrone, L., Zargeh, C., Varieties of Null-Filiform Leibniz algebras under the action of Hopf algebras, Algebra and Representation Theory, 26 (2023), 631-648. https://doi.org/10.1007/s10468-021-10105-2
• Demir, I., Misra, K. C., Stitzinger, E., On some structures of Leibniz algebras, Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics Contemporary Mathematics, 623 (2014), 41-54. https://doi.org/10.1090/conm/623/12456
• Jacobson, N., A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc., 6 (1955), 281-283. https://doi.org/10.1090/S0002-9939-1955-0068532-9
• Jacobson, N., Lie Algebras, Dover Publications Interscience, 1979.
• Ladra, M., Rikhsiboev, I. M., Turdiboev, R. M., Automorphisms and derivations of Leibniz algebras, Ukrains’kyi Matematychnyi Zhurnal, 68(7) (2016), 933-944. https://umj.imath.kiev.ua/index.php/umj/article/view/1891
• Loday, J. L., Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseing. Math., 39 (1993), 269-293. https://doi.org/10.5169/seals-60428
• Loday, J.L., Pirashvili, T., Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann., 269(1) (1993), 139-158. https://doi.org/10.1007/BF01445099
• Mansuroğlu, N., Fundamentals of Lie Algebras, Gece Kitaplığı, 2022.
• Mansuroğlu, N., Özkaya, M., On the structure constants of Leibniz algebras, International Advanced Research Journal in Science, Engineering and Technology, 5(5) (2018), 67-69. Doi:10.17148/IARJSET.2018.5511
• Sato, T., The derivations of the Lie algebras, Tohoku Math. Jour., 23, (1971), 21-36.
• Shahryari, M., A note on derivations of Lie algebras, Rev. Mat. Bull. Aust. Math. Soc., 84 (2011), 444-446. https://doi.org/10.1017/S0004972711002516
• Zargeh, C., Some remarks on derivations of Leibniz algebras, International Journal of Algebra, 6(30) (2012), 1471-1474. https://api.semanticscholar.org/CorpusID:131761265