Local derivation on solvable Lie algebras with naturally graded filiform nilradicals
Загрузки
В настоящей работе мы исследуем дифференцирования и локальные дифференцирования ко-
нечномерных разрешимых алгебр Ли, нильрадикалы, являющиеся естественно градуирован-
ными филиформными нильрадикалами. В частности устанавливается общий вид матриц, за-
дающих дифференцирования и локальные дифференцирования этих алгебр. Мы показываем,
что в указанных алгебрах существуют локальные дифференцирования, не сводящиеся к диф-
ференцированиям.
1. Ancochea Bermúdez J. M., Campoamor-Stursberg R., Garc´ıa Vergnolle L., Solvable Lie algebras with
naturally graded nilradicals and their invariants. Journal of Physics A: Mathematical and Theoretical,
2006, V. 6(39), P. 1339–1355.
2. Alauadinov A. K., Yusupov B. B., Local derivations of conformal Galilei algebra. Communications in
Algebra, 2024 V. 6(52), P. 2489–2508.
3. Ayupov Sh., Elduque A. and Kudaybergenov K., Local derivations and automorphisms of Cayley algebras.
Journal of Pure and Applied Algebra, 2023 V. 5(227), 107277.
4. Ayupov Sh., Khudoyberdiyev A., Local derivations on solvable Lie algebras. Linear and Multilinear
Algebra, 2021, V.7(69), P. 1286–1301.
5. Ayupov Sh., Khudoyberdiyev A., Yusupov B., Local and 2-local derivations of solvable Leibniz algebras.
International Journal of Algebra and Computation, 2020, V. 6(30), P. 1185–1197.
6. Ayupov Sh., Kudaybergenov K., I. Rakhimov, 2-Local derivations on finite-dimensional Lie algebras.
Linear Algebra and its Applications, 2015, 474, P. 1–11.
7. Ayupov Sh., Kudaybergenov K., Local derivations on finite-dimensional Lie algebras. Linear Algebra and
its Applications, 2016, 493, P. 381–398.
8. Ayupov Sh., Kudaybergenov K., Omirov B., Local and 2-local derivations and automorphisms on simple
Leibniz algebras. Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43, P. 2199–2234.
9. Ayupov Sh., Kudaybergenov K., Yusupov B., Local and 2-Local Derivations of Locally Simple Lie Algebras.
Journal of Mathematical Sciences, 2024, V.4(278), P. 613–622.
10. Ayupov Sh., Kudaybergenov K., Yusupov B., 2-Local derivations on generalized Witt algebras. Linear and
Multilinear Algebra, 2021, V. 16(69), P. 3130–3140.
11. Ayupov Sh., Yusupov B., 2-local derivations of infinite-dimensional Lie algebras. Journal of Algebra and
its Applications, 2020, V. 5(19), 2050100.
12. Chen Q.F., He Y., 2-local derivations on the planar Galilean conformal algebra. International Journal of
Mathematics, 2023 V. 5(34), 2350023.
13. Chen Z., Wang D., 2-Local automorphisms of finite-dimensional simple Lie algebras. Linear Algebra and
its Applications, 2015, 486, P. 335–344.
14. Chen Y., Zhao K., Zhao Y., Local derivations on Witt algebras. Linear and Multilinear algebra, 2022, V.
6(70), P. 1159–1172.
15. Jiang Q., Tang X., 2-Local derivations on the Schrödinger-Virasoro algebra. Linear and Multilinear
Algebra. 2023, V. 8(72), P. 1328–1345.
16. Kadison R., Local derivations, Journal of Algebra. 1990, 130, P. 494–509.
17. Kaygorodov I., Kudaybergenov K., Yuldashev I., Local derivations of semisimple Leibniz algebras.
Communication in Mathematics. 2022, V. 2(30), P. 1–12.
18. Kudaybergenov K., Omirov B., Kurbanbaev T., Local derivations on solvable Lie algebras of maximal
rank. Communications in Algebra, 2022, V. 9(50), P. 1-11.
19. Khudoyberdiyev A. Kh., Yusupov B. B., Local and 2-local
1
2 -derivation on finite-dimensional Lie algebras.
Results in Mathematics, 2024, 79,210.
20. Mamadaliyev U. Kh., Sattarov A., Yusupov B. B., Local and 2-local
1
2 -derivations of solvable Leibniz
algebras. Eurasian Mathematical Journal, 2025 V. 16(2), P. 1–14.
21. Larson D., Sourour A., Local derivations and local automorphisms of B(X). Proceedings of Symposia in
Pure Mathematics, 1990, 51, P. 187–194.
22.
ˇ
Semrl P., Local automorphisms and derivations on B(H). Proceedings of the American Mathematical
Society, 1997, 125, P. 2677–2680.
23. Е nobl L., Winternitz P., A class of solvable Lie algebras and their Casimir invariants. Journal of Physics
A: Mathematical and Theoretical, 2005, V. 12(38), P. 2687–2700.
24. X. Tang, M. Xiao, P. Wang, Local properties of Virasoro-like algebra. Journal of Geometry and Physics,
2023, 186, 104772.
25. Vergne M., Cohomologie des alg` ebres de Lie nilpotentes. Application à l´ etude de la vari´ et´ e des alg` ebres
de Lie nilpotentes. Bulletin de la Soci´ et´ e Math´ ematique de France, 1970, 98, P. 81–116,
26. Yao Y. F., Local derivations on the Witt algebra in prime characteristic. Linear and multilinear algebra,
2022, V. 15(70), P. 2919–2933.
27. Yao Y., Zhao K., Local properties of Jacobson-Witt algebras, Journal of Algebra,2021, 586, P. 1110–1121.
28. Yu Y., Chen Zh., Local derivations on Borel subalgebras of finite-dimensional simple Lie algebras.
Communications in Algebra, 2020, V. 1(48), P. 1–10.
29. Yusupov B., Vaisova N. and Madrakhimov T. Local
1
2 -derivation on of n-dimensional naturally graded
quasi-filiform Leibniz algebra of type I. AIP Conference Proceedings, 2024, 3147(1), 020008.
Copyright (c) 2025 «ВЕСТНИК НУУз»
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial-ShareAlike» («Атрибуция — Некоммерческое использование — На тех же условиях») 4.0 Всемирная.
.jpg)
2.png)
