Abstract
Let \(\mathfrak {g}\) be a complex simple Lie algebra. We consider subalgebras \(\mathfrak {m}\) which are Levi factors of parabolic subalgebras of \(\mathfrak {g}\), or equivalently \(\mathfrak {m}\) is the centralizer of its center. We introduced the notion of admissible systems on finite order \(\mathfrak {g}\)-automorphisms đ, and show that đ has admissible systems if and only if its fixed point set is a Levi factor. We then use the extended Dynkin diagrams to characterize such automorphisms, and look for automorphisms of minimal order.
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15 June 2021
Updating the Open Access funding note to fullfill the contractual requirement of the Multiple Compact agreement.
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Acknowledgements
M. K. Chuah is supported by a grant from the Ministry of Science and Technology of Taiwan. The authors are very grateful to the referee for providing many helpful suggestions, and to I. Dimitrov for engaging in useful discussions. The authors wish to thank the Mathematics Departments of University of Bologna and National Tsing Hua University for providing warm hospitalities during their mutual visits.
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Presented by: Vyjayanthi Chari
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Chuah, MK., Fioresi, R. Levi Factors and Admissible Automorphisms. Algebr Represent Theor 25, 341â358 (2022). https://doi.org/10.1007/s10468-020-10024-8
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DOI: https://doi.org/10.1007/s10468-020-10024-8