Involutive root-graded Lie algebras and Lie tori of type $A$

Abstract

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

To appear in Publications of the Research Institute for Mathematical Sciences