Geodesic
Almost inner derivations of some Leibniz algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 457-474.

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The present paper is devoted to almost inner derivations of thin and solvable Leibniz algebras. Namely, we consider a thin Lie algebra, solvable Lie algebra with nilradical natural graded filifform Lie algebra, natural graded thin Leibniz algebra, thin non-Lie Leibniz algebra and solvable Leibniz algebra with nilradical nul-filiform algebra. We prove that any almost inner derivations of all these algebras are inner derivations.
Keywords: Lie algebra, Leibniz algebra, thin Lie algebra, thin Leibniz algebra, derivation, inner derivation, almost inner derivation.
Mots-clés : solvable algebra, nilradical 
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Tuuelbay K. Kurbanbaev. Almost inner derivations of some Leibniz algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 457-474. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a4/

[1] K.K.Abdurasulov, B.A.Omirov, Maximal solvable extensions of finite-dimensional nilpotent Lie algebras, 17 Nov 2021, arXiv: 2111.07651v2 [math.RA]

[2] J.Adashev, T.Kurbanbaev, “Almost inner derivations of some nilpotent Leibniz algebras”, Journal of Siberian Federal University. Mathematics and Physics, 13:6 (2020), 733–745 | DOI | MR

[3] Sh.A.Ayupov, K.K.Kudaybergenov, “Local derivations on finite-dimensional Lie algebras”, Linear Algebra and its Applications, 493 (2016), 381–398 | DOI | MR | Zbl

[4] Sh.A.Ayupov, K.K.Kudaybergenov, “Local automorphisms on finite-dimensional Lie and Leibniz algebras”, Algebra, Complex Analysis, and Pluripotential Theory, 264, 2018 | MR | Zbl

[5] Sh.A.Ayupov, O. B. Amirov, “On some classes of nilpotent Leibniz algebras”, Siberian Math. J., 42:1 (2001), 15–24 | DOI | MR | Zbl

[6] Sh.Ayupov, B.Yusupov, “2-Local derivations of infinite-dimensional Lie algebras”, Journal of Algebra and Its Applications, 19:05 (2050), 2050100 | DOI | MR

[7] D.Burde, K.Dekimpe, B.Verbeke, “Almost inner derivation of Lie algebras”, Journal of Algebra and Its Applications, 17:11 (2018) | DOI | MR | Zbl

[8] D.Burde, K.Dekimpe, B.Verbeke, “Almost inner derivations of Lie algebras II”, International Journal of Algebra and Computation, 31:02 (2021), 341–364 | DOI | MR | Zbl

[9] E.M.Cañete, Kh.A.Khudoyberdiyev, “The classification of 4-dimensional Leibniz algebras”, Linear Algebra and its Applications, 439 (2013), 273–288 | DOI | MR

[10] M.Goze, Y.Khakimdjanov, Nilpotent Lie algebras, Mathematics and its Applications, 361, Kluwer Academic Publishers Group, Dordrecht, 1996 | MR | Zbl

[11] J.M.Casas, M.Ladra, B.A.Omirov, I.A.Karimjanov, “Classification of solvable Leibniz algebras with null-filiform nilradical”, Linear and Multilinear Algebra, 61:6 (2012), 758–774 | DOI | MR

[12] A.Fialowski, “Classification of Graded Lie Algebras with Two Generators”, Moscow University Mathematics Bulletin, 38:2 (1983), 76–79 | MR | Zbl

[13] C.S.Gordon, E.N.Wilson, “Isospectral defermations of compact solvmanifolds”, J. Diferential Geom., 19:1 (1984), 214–256 | MR

[14] B.A.Omirov, “Thin Leibniz Algebras”, Mathematical Notes, 80:2 (2006), 244–253 | DOI | MR | Zbl

[15] L.Šnobl, P.Winternitz, “A class of solvable Lie algebras and their Casimir invariants”, J. Phys. A, 38:12 (2005), 2687–2700 | DOI | MR