LOCAL DERIVATIONS OF METABELIAN FILIFORM LIE ALGEBRAS
Abstract
Let be an algebra (not necessary associative). Recall that a linear mapping is said to be a derivation, if for all A linear mapping is said to be a local derivation, if for every there exists a derivation on (depending on ) such that
References
K.K. Abdurasulov, B.A. Omirov, Maximal solvable extensions of a pure non-characteristically nilpotent Lie algebra, Preprint, arXiv:2111.07651 [math.RA].
Sh.A. Ayupov, A. Khudoyberdiyev, B.B. Yusupov, Local and 2-local derivations of solvable Leibniz algebras, Internat. J. Algebra Comput., 30:6 (2020) 1185-1197.
Sh.A. Ayupov, K.K. Kudaybergenov, Local derivations on finite-dimensional Lie algebras, Linear Algebra Appl., 493 (2016) 381-398.
Sh. A. Ayupov, K. K. Kudaybergenov, A. Allambergenov, Local and 2-local derivations on octonion algebras, Journal of algebra and its applications, https://doi.org/10.1142/S0219498823501475.
Y. Chen, K. Zhao, Y. Zhao, Local derivations on Witt algebras, Linear and multilinear algebra, 70:6 (2022) 1159–1172.
A.P. Elisova, I.N. Zotov, V.M. Levchuk and G.S. Suleymanova, Local automorphisms and local derivations of nilpotent matrix algebras, Izv. Irkutsk Gos. Univ., 4:1 (2011) 9-19.
B.E. Johnson, Local derivations on -algebras are derivations, Transactions of the American Mathematical Society, 353 (2001) 313–325.
J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer, New York, 1972.
M. Goze, Y. Khakimdjanov, Nilpotent Lie algebras. Kluwer Academic Publishers Group, Dordrecht (1996), xvi + 336 pp.
M. Goze, Y. Khakimdjanov, Nilpotent and solvable Lie algebras. Handbook of algebra, Vol. 2, 615-663, Handb. Algebr., 2, Elsevier/North-Holland, Amsterdam, 2000.
R.V. Kadison, Local derivations, J. Algebra, 130 (1990) 494-509.
D. R. Larson, A. R. Sourour, Local derivations and local automorphisms of , Proc. Sympos. Pure Math., 51 (1990) 187-194.
K.K. Kudaybergenov, B.A. Omirov, T.K. Kurbanbaev, Local derivations on solvable Lie algebras of maximal rank, Communications in Algebra 50:9 (2022) 1-11.
D.J. Meng, L.Sh. Zhu, Solvable complete Lie algebras. I., Comm. Algebra. 24:13 (1996) 4181-4197.
L. Šnobl, On the structure of maximal solvable extensions and of Levi extensions of nilpotent Lie algebras, J. Phys. A, Math. Theor. 43:17 (2010) Article ID 505202.
B. Verbeke, Almost-inner derivations of Lie algebras, Master dissertation, KU Leuven – Faculty of Science, 2016.
B. Verbeke, Almost inner derivations of Lie algebras, PhD dissertation, KU Leuven – Faculty of Science, 2020.
Y. Yu, Zh. Chen, Local derivations on Borel subalgebras of finite-dimensional simple Lie algebras, Comm. Algebra 48:1 (2020) 1-10.
Y. F. Yao, Local derivations on the Witt algebra in prime characteristic, Linear and multilinear algebra https://doi.org/10.1080/03081087.2020.1819189.
