Levi Factors and Admissible Automorphisms

Let g be a complex simple Lie algebra. We consider subalgebras m which are Levi factors of parabolic subalgebras of g , or equivalently m is the centralizer of its center. We introduced the notion of admissible systems on finite order g -automorphisms 𝜃 , and show that 𝜃 has admissible systems if an...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 25; no. 2; pp. 341 - 358
Main Authors Chuah, Meng-Kiat, Fioresi, Rita
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2022
Springer Nature B.V
Subjects
Associative Rings and Algebras
Automorphisms
Commutative Rings and Algebras
Fixed points (mathematics)
Lie groups
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
17B22
Automorphism
Levi factor
Admissible system
17B40
17B20
Dynkin diagram
Complex simple Lie algebra
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Summary:Let g be a complex simple Lie algebra. We consider subalgebras m which are Levi factors of parabolic subalgebras of g , or equivalently m is the centralizer of its center. We introduced the notion of admissible systems on finite order g -automorphisms 𝜃 , and show that 𝜃 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.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-020-10024-8