Almost inner derivations of Leibniz algebras

This talk investigates almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations in non-Lie filiform Leibniz algebras which are different from inner derivations. Moreover, we analyze almost inner derivations in graded thin Leibniz algebras, thin non-Lie Leibniz algebras, and solvable Leibniz algebras whose nilradical is null filiform algebra, proving that that every almost inner derivation of these algebras is an inner derivation. In addition, we study almost inner derivations of finite-dimensional simple Leibniz algebras. We study almost internal derivations of a simple Leibniz algebra of the form $s{{l}_{2}}\dot{+}I$. Also we prove that every almost inner derivation of a simple Leibniz algebra $s{{l}_{2}}\dot{+}I$ is inner and we find conditions for the existence of almost inner derivations on finite-dimensional simple Leibniz algebras for which is not inner derivations.