The Graded Algebras with a Graded Identity of Degree 2

This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree $2$. % Let $\mathsf{G}$ be a finite abelian group, $\mathbb{F}$ a field of characteristic zero and $\mathfrak{A}$ a $\mathsf{G}$-graded $\mathbb{F}$-algebra. % We prove that, for $\m