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Here is a exercise in the Eiichi Abe's book Hopf Algebras, Ex2.4,Ch2, p.83.

If $X$ is a left coideal, show that $X\wedge Y$ is a right coideal and that $X\subset X\wedge Y$.

Maybe you can explain the $X\wedge Y$ in the Hopf algebra, does it has any geometry meaning?

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This is not the exterior product. –  Berci Jan 28 '13 at 12:49

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