2023/02/01 by Azam, Saeid, Izadi, Mehdi Farhadi · 4 citations
#17B67 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2302.00446
In finite-dimensional simple Lie algebras and affine Kac-Moody Lie algebras, Chevalley involutions are crucial ingredients of the modular theory. Towards establishing the modular theory for extended affine Lie algebras, we investigate the existence of ``Chevalley involutions" for Lie tori and extended affine Lie algebras. We first discuss how to lift a Chevalley involution from the centerless core which is characterized to be a centerless Lie torus to the core and then to the entire extended affine Lie algebra. We then prove that each centerless Lie torus of reduced type admits a Chevalley involution.