# The cortex of a class of semidirect product exponential Lie groups

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https://doi.org/10.33044/revuma.2793## Abstract

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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