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

Document Type: Research Paper

Authors

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 $\alpha\in\mathrm{Der}(L)$ 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.

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Volume 43, Issue 1
January and February 2017
Pages 79-93
  • Receive Date: 25 November 2014
  • Revise Date: 13 October 2015
  • Accept Date: 14 October 2015