The cortex of a class of semidirect product exponential Lie groups


  • Béchir Dali Department of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, 7021 Jarzouna, Bizerte, Tunisia
  • Chaïma Sayari Department of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, 7021 Jarzouna, Bizerte, Tunisia



In the present paper, we are concerned with the determination of the cortex of semidirect product exponential Lie groups. More precisely, we consider a finite dimensional real vector space $V$ and some abelian matrix group $H=\exp\big(\sum_{i=1}^{n}\mathbb{R} A_i\bigr)$, where $\{A_1,\dots, A_n\}$ is a set of pairwise commuting non-singular matrices acting on $V$. We first investigate the cortex of the action of the group $H$ on $V$. As an application, we investigate the cortex of the group semidirect product $G:=V\rtimes\mathbb{R}^n$.


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