On dimension of a special subalgebra of derivations of nilpotent Lie algebras
S. Sheikh-Mohseni
F. Saeedi
Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran.
‎Let $L$ be a Lie algebra‎, ‎$\mathrm{Der}(L)$ be the set of all derivations of $L$ and $\mathrm{Der}_c(L)$ denote the set of all derivations $\alpha\in\mathrm{Der}(L)$ for which $\alpha(x)\in [x,L]:=\{[x,y]\vert y\in L\}$ for all $x\in L$‎. ‎We obtain an upper bound for dimension of $\mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classify all finite dimensional nilpotent Lie algebras $L$ over algebraically closed fields for which dim$\mathrm{Der}_c(L)$ attains its maximum value.
Lie algebra‎
‎derivation‎
‎nilpotent Lie algebra‎
17-XX Nonassociative rings and algebras
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January and February 2017
Receive Date: 25 November 2014
Sheikh-Mohseni, S., Saeedi, F. (2017). On dimension of a special subalgebra of derivations of nilpotent Lie algebras. Bulletin of the Iranian Mathematical Society, 43(1), 79-93.
S. Sheikh-Mohseni; F. Saeedi. "On dimension of a special subalgebra of derivations of nilpotent Lie algebras". Bulletin of the Iranian Mathematical Society, 43, 1, 2017, 79-93.
Sheikh-Mohseni, S., Saeedi, F. (2017). 'On dimension of a special subalgebra of derivations of nilpotent Lie algebras', Bulletin of the Iranian Mathematical Society, 43(1), pp. 79-93.
Sheikh-Mohseni, S., Saeedi, F. On dimension of a special subalgebra of derivations of nilpotent Lie algebras. Bulletin of the Iranian Mathematical Society, 2017; 43(1): 79-93.