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I had a quick question. I apologize if it has already been asked. Let $G$ be a split reductive group over a field $k$ and let $G'$ be it's derived group. It is well-know that root systems of $G'$ and $G$ are identified using the natural map between the corresponding character lattices. Does it mean that they are isomorphic as root systems, e.g, simple roots, positive roots, Weyl groups are identified as well?

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