LOCAL DERIVATIONS ON SOLVABLE LIE ALGEBRAS WITH A FILIFORM NILRADICAL
Keywords:
Lie algebra, derivation, local derivationAbstract
The present paper is devoted to the description of local derivations on rank one or zero solvable Lie algebras with the filiform nilradical. Firstly, we shall consider local derivations of rank one solvable Lie algebra and with the filiform nilradical and Namely, we find a general form of local derivations in the case of solvable Lie algebras whose nilradical is the Witt algebra and special filiform algebra In particular, in these cases the spaces are Lie algebras. Finally, we shall find a general form of rank zero solvable Lie algebra with a metabelian filifrom nilradical.
References
J.M. Ancochea, R.Campoamor-Stursberg, L. Garcia Vergnolle, Solvable Lie algebras with naturally graded nilradicals and their invariants, J. Phys. A, Math. Theor. 39 (2006), 1339-1355.
Sh.A. Ayupov, K.K. Kudaybergenov, Local derivations on finite-dimensional Lie algebras, Linear Algebra Appl. 493 (2016), 381-398.
Sh.A. Ayupov, A.Kh. Khudoyberdiyev, Local derivations on solvable Lie algebras, Linear and Multilinear Algebra 69 (2021), no. 7, 1286-1301.
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.
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.
D.J. Meng, L.Sh. Zhu, Solvable complete Lie algebras. I. Comm. Algebra 24 (1996), no. 13, 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 (2010), 17, Article ID 505202.
L. Šnobl, Maximal solvable extensions of filiform algebras Arch. Math. (Brno) 47 (2011), no. 5, 405-414.
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 (2020), no. 1, 1-10.
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
