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Answer by Chris for Dimension of tensor product vs. dimension of direct product

Well, first, as Lie groups, it does not in full generality really make sense to take tensor products. Given a two Lie groups, we take their cartesian product (also known as direct product) which is...

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Answer by joriki for Dimension of tensor product vs. dimension of direct product

It seems to me that one thing you’re confusing is groups and their representations. There’s no such thing as a tensor product of groups, so $SU(2)\otimes SU(2)$ makes no sense. There are various...

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Dimension of tensor product vs. dimension of direct product

I am really sorry if this is trivial but I come from Physics and it is really confusing for me to understand what is going on and looking at the answers on both Physics and Math SE sent me through a...

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