On dimension of a special subalgebra of derivations of nilpotent Lie algebras

Authors

  • F. Saeedi Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran.
  • S. Sheikh-Mohseni Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran.
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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