On $(\alpha ,1,0)$-derivations of anti-commutative algebras

Abstract

We solve an open problem concerning the well-known $(\alpha ,\beta ,\gamma )$-derivations, proving that the spaces of $(\alpha ,1,0)$-derivations of any Lie algebra are isomorphic ($\alpha \ne 0,1$). Also, we prove sharp bounds for the invariants functions defined by such spaces.

9 pages. All comments or suggestions are most welcome