@article{Messaoud_Rahali_2020, title={Another proof for the continuity of the Lipsman mapping}, volume={72}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/548}, DOI={10.37863/umzh.v72i7.548}, abstractNote={<p>UDC 515.1</p> <p>We consider the semidirect product $G = K \ltimes V$ where $K$ is a connected compact Lie group acting by automorphisms on a finite dimensional real vector space $V$ equipped with an inner product $\langle , \rangle$. By $\hat G $ we denote the unitary dual of $G$ and by ${\mathfrak{g}^{ \ddagger} /} G$ the space of admissible coadjoint orbits, where $\mathfrak{g}$ is the Lie algebra of $G$. It was pointed out by Lipsman that the correspondence between $\hat{G} $ and ${\mathfrak{g}^{ \ddagger} /} G$ is bijective. Under some assumption on $G$, we give another proof for the continuity of the orbit mapping (Lipsman mapping)<br>$$\Theta : {\mathfrak{g}^{ \ddagger} /} G - \rightarrow \hat{G} .$$</p>}, number={7}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Messaoud, A. and Rahali, A.}, year={2020}, month={Jul.}, pages={945-951} }