Abstract
For a classical group G over a field F together with a finite-order automorphism θ that acts compatibly on F, we describe the fixed point subgroup of θ on G and the eigenspaces of θ on the Lie algebra \(\mathfrak{g}\) in terms of cyclic quivers with involution. More precise classification is given when \(\mathfrak{g}\) is a loop Lie algebra, i.e., when F = ℂ((t)).
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The second author was supported by the Packard Foundation.
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Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday
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Yang, J., Yun, Z. Semilinear automorphisms of classical groups and quivers. Sci. China Math. 62, 2355–2370 (2019). https://doi.org/10.1007/s11425-019-1612-8
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DOI: https://doi.org/10.1007/s11425-019-1612-8