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Let $G$ be an algebraic closed subgroup of $SL(n,\mathbb{R})$ whose action on $\mathbb{R}^d$$\mathbb{R}^n$ is strongly irreducible, i.e. there is no finite union of proper nonzero linear subspaces of $\mathbb{R^n}$ which is invariant under $G$. Is it true that $G$ is semisimple?

Let $G$ be an algebraic closed subgroup of $SL(n,\mathbb{R})$ whose action on $\mathbb{R}^d$ is strongly irreducible. Is it true that $G$ is semisimple?

Let $G$ be an algebraic closed subgroup of $SL(n,\mathbb{R})$ whose action on $\mathbb{R}^n$ is strongly irreducible, i.e. there is no finite union of proper nonzero linear subspaces of $\mathbb{R^n}$ which is invariant under $G$. Is it true that $G$ is semisimple?

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Strongly Irreducible Action implies Semisimplicity

Let $G$ be an algebraic closed subgroup of $SL(n,\mathbb{R})$ whose action on $\mathbb{R}^d$ is strongly irreducible. Is it true that $G$ is semisimple?