Salvato in:
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Autore principale: Sherman, Alexander
Natura: Preprint
Pubblicazione: 2020
Soggetti:
Accesso online:https://arxiv.org/abs/2004.03095
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Sommario:
  • Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $θ$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $θ$ or $δ\circθ$ admits an Iwasawa decomposition, where $δ$ is the canonical grading automorphism $δ(x)=(-1)^{\overline{x}}x$. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$.