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Almost inner derivations of Leibniz algebras

Year 2024, Volume: 73 Issue: 4, 969 - 981
https://doi.org/10.31801/cfsuasmas.1485446

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.

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
Year 2024, Volume: 73 Issue: 4, 969 - 981
https://doi.org/10.31801/cfsuasmas.1485446

Abstract

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
There are 16 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research Articles
Authors

Nil Mansuroğlu 0000-0002-6400-2115

Mücahit Özkaya 0000-0002-6436-8360

Publication Date
Submission Date May 17, 2024
Acceptance Date October 21, 2024
Published in Issue Year 2024 Volume: 73 Issue: 4

Cite

APA Mansuroğlu, N., & Özkaya, M. (n.d.). Almost inner derivations of Leibniz algebras. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 969-981. https://doi.org/10.31801/cfsuasmas.1485446
AMA Mansuroğlu N, Özkaya M. Almost inner derivations of Leibniz algebras. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):969-981. doi:10.31801/cfsuasmas.1485446
Chicago Mansuroğlu, Nil, and Mücahit Özkaya. “Almost Inner Derivations of Leibniz Algebras”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 4 n.d.: 969-81. https://doi.org/10.31801/cfsuasmas.1485446.
EndNote Mansuroğlu N, Özkaya M Almost inner derivations of Leibniz algebras. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 969–981.
IEEE N. Mansuroğlu and M. Özkaya, “Almost inner derivations of Leibniz algebras”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 4, pp. 969–981, doi: 10.31801/cfsuasmas.1485446.
ISNAD Mansuroğlu, Nil - Özkaya, Mücahit. “Almost Inner Derivations of Leibniz Algebras”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (n.d.), 969-981. https://doi.org/10.31801/cfsuasmas.1485446.
JAMA Mansuroğlu N, Özkaya M. Almost inner derivations of Leibniz algebras. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;73:969–981.
MLA Mansuroğlu, Nil and Mücahit Özkaya. “Almost Inner Derivations of Leibniz Algebras”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 4, pp. 969-81, doi:10.31801/cfsuasmas.1485446.
Vancouver Mansuroğlu N, Özkaya M. Almost inner derivations of Leibniz algebras. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):969-81.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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