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Outer automorphism groups of real forms of contragredient Lie superalgebras
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Outer automorphism groups of real forms of contragredient Lie superalgebras

Meng-Kiat ChuahMingjing Zhang
Journal of Algebra, 卷.619, 頁碼.60-98
04/2023

摘要

Cartan automorphism Contragredient Lie superalgebra Dynkin diagram Kac diagram Outer automorphism group Real form Algebra and Number Theory
Let g be a real form of a contragredient Lie superalgebra. Let Aut(g) be the group of g-automorphisms, and let Int(g) be its identity component. We define the outer automorphism group of g by Out(g)=Aut(g)/Int(g). The Kac diagrams are generalizations of Dynkin diagrams, and they represent the even part g . The Cartan automorphisms are generalizations of Cartan involutions, and they represent g. We express Out(g) in terms of diagram symmetries on the Kac diagrams and Cartan automorphisms. As a result, we obtain Out(g) for all real forms of contragredient Lie superalgebras.

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