Specht property of varieties of graded Lie algebras

Let $$UT_n(F)$$ be the algebra of $$n\times n$$ upper triangular matrices and denote $$UT_n(F)^{(-)}$$ Lie on vector space with respect to usual bracket (commutator), over an infinite field F. In this paper, we give a positive answer Specht property for ideal $$\mathbb {Z}_n$$ -graded identities canonical grading when characteristic p F is 0 or larger than $$n-1$$ . Namely prove that every graded in free contains , finitely based. Moreover show if $$p=2$$ then {Z}_3$$ $$UT_3^{(-)}(F)$$ do not satisfy property. More precisely, construct explicitly containing which generated as identities.