L-Iwasawa Decomposition of the Generalized Lorentz Group

E. N. Reyes

Journal of Lie theory, Tome 32 (2022) no. 4, pp. 1187-1196

Résumé

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 $G=ke^{tV_1}e^Y$.

Détail

Classification : 15A23, 22E15
Mots-clés : Involution, Iwasawa decomposition, Lorentz group