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Journal of Lie Theory 32 (2022), No. 4, 1187--1196
Copyright Heldermann Verlag 2022

L-Iwasawa Decomposition of the Generalized Lorentz Group

Edgar N. Reyes
Department of Mathematics, Southeastern Louisiana University, Hammond, Louisiana, U.S.A.


Let $n\geq 2$. Let $O(1,n)$ be the generalized Lorentz Lie group, and let $\mathfrak{so}(1,n)$ be its Lie algebra. Let $L=diag(1,-1,I_{n-1})$ be a diagonal matrix. We state a sufficient condition that if satisfied by $G\in O(1,n)$ then there exists $t\in \mathbb{R}$, $k\in O(1,n)$, $V_1, Y\in \mathfrak{so}(1,n)$ such that $LkL^{-1}=k$, $V_1\neq 0$, $LV_1L^{-1}=-V_1$, $[V_1,Y]=Y$, and $G=ke^{tV_1}e^Y$.

Keywords: Involution, Iwasawa decomposition, Lorentz group.

MSC: 15A23, 22E15.

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