Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 32 (2022), No. 4, 973--996Copyright Heldermann Verlag 2022 Iwasawa Decomposition for Lie Superalgebras Alexander Sherman Dept. of Mathematics, University of California, Berkeley, U.S.A. xandersherm@gmail.com [Abstract-pdf] Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $\theta$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that at least one of $\theta$ or $\delta\circ\theta$ admits an Iwasawa decomposition, where $\delta$ is the canonical grading automorphism $\delta(x)=(-1)^{\overline{x}}x$. 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 $\mathfrak{g}$. Keywords: Lie superalgebras, symmetric pairs, root systems. MSC: 17B22, 17B20, 17B40. [ Fulltext-pdf  (200  KB)] for subscribers only.