Let $(G,*)$ and $(H,.)$ be two Lie groups. I want to show that the product manifold $GXH$ has the structure of a Lie group. I know that if $G$ and $H$ are two manifold so $GXH$ must be manifold. What must I do?
2026-04-08 11:24:08.1775647448
Lie Group and product manifold
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You have to show that the product and the inversion are differentiable in $G\times H$. This is a consequence of the fact that the product of differentiable maps are differentiable.