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 ($\alpha\neq 0,1$). Also, we prove sharp bounds for the invariants functions defined by such spaces.