TY - JOUR
AU - A. Messaoud
AU - A. Rahali
PY - 2020/07/15
Y2 - 2020/08/12
TI - Another proof for the continuity of the Lipsman mapping
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 7
SE - Research articles
DO - 10.37863/umzh.v72i7.548
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/548
AB - UDC 515.1We 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)$$\Theta : {\mathfrak{g}^{ \ddagger} /} G - \rightarrow \hat{G} .$$
ER -