Involutive root-graded Lie algebras and Lie tori of type $A$
Saeid Azam, Mehdi Izadi Farhadi
TL;DR
This paper characterizes all centerless Lie tori of type A that admit a Chevalley involution, extending previous results and deepening understanding of involutions in root-graded Lie algebras.
Contribution
It provides a complete characterization of centerless Lie tori of type A with Chevalley involutions, advancing the theory of involutions in root-graded Lie algebras.
Findings
Characterization of all centerless Lie tori of type A with Chevalley involution
Extension of previous results to non-reduced types
Complete classification of involutions in this context
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 admitting a Chevalley involution. This work extends and completes the earlier results regarding the existence of such involutions for Lie tori of reduced types.
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