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Different Bialgebra/Hopf algebra structures on coalgebras

Then put algebra structures on this as follows: $xy=yx$ $y^2 = 0$ either $x^2 = 0$ or $x^2 = y$ This gives two graded (with $\deg x = 1$, $\deg y = 2$) connected cocommutative bialgebras, and so by a …
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