I have familiarized myself with various definitions (one-dimensionality of simple left comodules, generated as an algebra by group-like and skew-like elements...) and examples of pointed Hopf algebras (small quantum groups, universal enveloping algebras of Lie algebras...) but I have yet to get an intuition for how the pointedness of a Hopf algebra affects its structure. I know there are several open questions about the structure of pointed Hopf algebras, but can anyone offer an explanation, perhaps with an example? It was mentioned that "pointedness" is like a weakening of cocommutativity, is this the best way to think about it?

(I have seen the other posts asking basic questions about pointed Hopf algebras, but they didn't quite address my question.)

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    $\begingroup$ mathoverflow.net/questions/86627/what-is-a-pointed-hopf-algebra $\endgroup$ – Carlo Beenakker Sep 26 '13 at 19:23
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    $\begingroup$ In the question addressed above, darij grinberg gave a very nice answer. Another approach to your question would be to try to understand the structure theorem of Andruskiewitsch and Schneider about finite-dimensional pointed Hopf algebras with abelian coradical. At the end, these pointed Hopf algebras are much like Lusztig's small quantum groups. $\endgroup$ – Leandro Vendramin Sep 26 '13 at 23:33

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