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

2025/08/23 by Azam, Saeid, Farhadi, Mehdi Izadi
#16W10 #17B65 #17B67 #17B70 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2508.16954

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_ℓ(ℓ≥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.

Citations

• Chevalley involutions for Lie tori and extended affine Lie algebras
• Integral structures in extended affine Lie algebras
• Cayley Polynomials
• Locally extended affine Lie algebras

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• Classification of quantum tori with involution
• A Course on Lie algebras and Chevalley groups
• On the construction of semisimple Lie algebras and Chevalley groups
• The Chevalley Involution and a Duality of Weight Varieties