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Science China Mathematics

, Volume 62, Issue 11, pp 2355–2370 | Cite as

Semilinear automorphisms of classical groups and quivers

  • Jinwei Yang
  • Zhiwei YunEmail author
Articles

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)).

Keywords

semilinear automorphisms classical groups quiver 

MSC(2010)

11E39 11E57 17B40 

Notes

Acknowledgements

The second author was supported by the Packard Foundation.

References

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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