On (α, 1, 0)-Derivations of Anti-Commutative Algebras

The aim of this paper is to investigate (, 1, 0)-derivations of anti-commutative algebras.We show that when the base field is of characteristic zero, the dimensions of the spaces of (, 1, 0)-derivations yield an infinite one-parameter family of invariant functions under algebra isomorphism.Furthermore, we demonstrate that this infinite family reduces to only three distinct functions when we restrict our focus to the class of Lie algebras.This reduction addresses an open problem regarding the behavior of these invariants in the context of Lie algebras.Additionally, we establish sharp bounds for these invariant functions.