Involutive Root-Graded Lie Algebras and Lie Tori of Type $A$

We investigate the concept of a “Chevalley involution” within the framework of root-graded Lie algebras with compatible grading. We provide a characterization of all centerless Lie tori of type A_{\ell} ( \ell\geq2 ) admitting a Chevalley involution. This work extends and completes the earlier results regarding the existence of such involutions for Lie tori of reduced types.