Journal of Lie Theory

no. 4
L-Iwasawa Decomposition of the Generalized Lorentz Group
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1187-1196
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 $G=ke^{tV_1}e^Y$.
DOI: 10.5802/jolt.1271
Classification: 15A23, 22E15
Keywords: Involution, Iwasawa decomposition, Lorentz group 
@article{JOLT_2022_32_4_a13,
     author = {E. N. Reyes},
     title = {L-Iwasawa {Decomposition} of the {Generalized} {Lorentz} {Group}},
     journal = {Journal of Lie Theory},
     pages = {1187--1196},
     year = {2022},
     volume = {32},
     number = {4},
     doi = {10.5802/jolt.1271},
     zbl = {1522.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1271/}
}
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E. N. Reyes. L-Iwasawa Decomposition of the Generalized Lorentz Group. Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1187-1196. doi: 10.5802/jolt.1271

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