Hermitian real forms of contragredient Lie superalgebras

For a complex semisimple Lie algebra g with Hermitian real form gR=kR+pR, there exists a positive system of roots such that the adjoint k-representation on p stabilizes the positive and negative root spaces. In this article, we extend this result to contragredient Lie superalgebras g, and study the...

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Bibliographic Details
Published inJournal of algebra Vol. 437; pp. 161 - 176
Main Authors Chuah, Meng-Kiat, Fioresi, Rita
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2015
Subjects
Contragredient Lie superalgebras
Hermitian real forms
17B22
Contragredient Lie superalgebras
Hermitian real forms
17B20
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Summary:For a complex semisimple Lie algebra g with Hermitian real form gR=kR+pR, there exists a positive system of roots such that the adjoint k-representation on p stabilizes the positive and negative root spaces. In this article, we extend this result to contragredient Lie superalgebras g, and study the number of irreducible components of the k-representation. We also discuss the complex structure on gR/kR.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2015.04.018