On dimension of a special subalgebra of derivations of nilpotent Lie algebras
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Abstract:
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 $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. 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.
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Journal title
volume 43 issue 1
pages 79- 93
publication date 2017-02-22
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