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 $A_{\mathrm{\ell }}(\mathrm{\ell }\ge 2)$ admitting a Chevalley involution. This work extends and completes the earlier results regarding the existence of such involutions for Lie tori of reduced types.