Geodesic
Local and 2-local derivations of locally simple Lie algebras
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 68 (2022) no. 1, pp. 59-69.

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In the present paper, we study local and 2-local derivations of the classical locally simple Lie algebras. Firstly, we prove that every local and 2-local derivations on classical locally simple Lie algebra is a derivation. Further, we show that every local derivation of Borel subalgebras of locally simple Lie algebras is a derivation. 
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Sh. Ayupov; K. Kudaybergenov; B. Yusupov. Local and 2-local derivations of locally simple Lie algebras. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 68 (2022) no. 1, pp. 59-69. http://geodesic.mathdoc.fr/item/CMFD_2022_68_1_a4/

[1] Albeverio S., Ayupov Sh. A., Kudaybergenov K. K., Nurjanov B. O., “Local derivations on algebras of measurable operators”, Commun. Cont. Math., 13:4 (2011), 643–657 | DOI | MR | Zbl

[2] Ayupov Sh. A., Khudoyberdiyev A. Kh., “Local derivations on Solvable Lie algebras”, Linear Multilinear Algebra, 69:7 (2021), 1286–1301 | DOI | MR | Zbl

[3] Ayupov Sh. A., Khudoyberdiyev A. Kh., Yusupov B. B., Local and 2-local derivations of solvable Leibniz algebras, 2019, arXiv: 1911.03733v1 [math.RA] | MR

[4] Ayupov Sh. A., Kudaybergenov K. K., “2-Local automorphisms on finite dimensional Lie algebras”, Linear Algebra Appl., 507 (2016), 121–131 | DOI | MR | Zbl

[5] Ayupov Sh. A., Kudaybergenov K. K., “Local derivation on finite dimensional Lie algebras”, Linear Algebra Appl., 493 (2016), 381–398 | DOI | MR | Zbl

[6] Ayupov Sh. A., Kudaybergenov K. K., Nurjanov B. O., Alauadinov A. K., “Local and 2-local derivations on noncommutative Arens algebras”, Math. Slovaca, 64:2 (2014), 423–432 | DOI | MR | Zbl

[7] Ayupov Sh. A., Kudaybergenov K. K., Omirov A. B., “Local and 2-local derivations and automorphisms on simple Leibniz algebras”, Bull. Malays. Math. Sci. Soc. (2), 43 (2020), 2199–2234 | DOI | MR | Zbl

[8] Ayupov Sh. A., Kudaybergenov K. K., Rakhimov I. S., “2-Local derivations on finite-dimensional Lie algebras”, Linear Algebra Appl., 474 (2015), 1–11 | DOI | MR | Zbl

[9] Ayupov Sh. A., Kudaybergenov K. K., Yusupov B. B., “2-Local derivations on generalized Witt algebras”, Linear Multilinear Algebra, 69:16 (2019), 3130–3140 | DOI | MR

[10] Ayupov Sh. A., Yusupov B. B., “2-local derivations on Virasoro algebras”, Bull. Nat. Univ. Uzbekistan. Math. Natural Sci., 2:4 (2019), 217–230 | MR

[11] Ayupov Sh. A., Yusupov B. B., “2-local derivations of infinite-dimensional Lie algebras”, J. Algebra Appl., 19:5 (2020), 2050100 | DOI | MR | Zbl

[12] Chen Z., Wang D., “2-Local automorphisms of finite-dimensional simple Lie algebras”, Linear Algebra Appl., 486 (2015), 335–344 | DOI | MR | Zbl

[13] Chen Y., Zhao K., Zhao Y., Local derivations on Witt algebras, 2019, arXiv: 1911.0515v1 [math.RA] | MR

[14] Dimitrov I., Penkov I., “Weight modules of direct limit Lie algebras”, Int. Math. Res. Not. IMRN., 199:5 (1999), 223–249 | DOI | MR

[15] Johnson B. E., “Local derivations on $C^*$-algebras are derivations”, Trans. Moscow Math. Soc., 353 (2001), 313–325 | DOI | MR | Zbl

[16] Kadison R. V., “Local derivations”, J. Algebra, 130 (1990), 494–509 | DOI | MR | Zbl

[17] Larson D. R., Sourour A. R., “Local derivations and local automorphisms of $B(X)$”, Operator theory, operator algebras and applications, Proc. of the summer research institute (University of New Hampshire, Durham, USA, July 3–23, 1988), Am. Math. Soc., Providence, 1990, 187–194 | DOI | MR | Zbl

[18] Nebb K.-H., “Derivations of locally simple Lie algebras”, J. Lie Theory, 15 (2005), 589–594 | MR

[19] Neeb K.-H., Stumme N., “On the classification of locally finite split simple Lie algebras”, J. Reine Angew. Math., 533 (2001), 25–53 | MR | Zbl

[20] Šemrl P., “Local automorphisms and derivations on $B(H)$”, Proc. Am. Math. Soc., 125 (1997), 2677–2680 | DOI | MR

[21] Yalong Yu., Chen Z., “Local derivations on Borel subalgebras of finite-dimensional simple Li algebras”, Commun. Algebra, 48:1 (2019), 1–10 | MR

[22] Yusupov B. B., “2-Local derivations on Witt algebras”, Uzbek Math. J., 2018, no. 2, 160–166 | DOI | MR | Zbl