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Chevalley involutions for Lie tori and extended affine Lie algebras (2302.00446v2)
Published 1 Feb 2023 in math.QA
Abstract: 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.