Timeline for Fundamental theorem of coalgebras

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Mar 12, 2012 at 8:11	comment	added	Fanf		Ok thanks for these comments. I have read several proofs of the theorem in the "classical case" of co-algebras. Matthew Daws, you point out what prevent me from adapting naively these proofs.
Mar 8, 2012 at 20:43	comment	added	Matthew Daws		van Daele uses multipliers-- so $A$ is a non-unital algebra, and we have a non-degenerate homomorphism $\Delta:A\rightarrow M(A\otimes A)$ from $A$ into the multiplier algebra of $A\otimes A$. Then you have to think what coassociative should mean, and what the counit should do. (Which are pretty obvious). Often you want some sort of "regularity" condition. It seems to me hard to generalise from the usual proof (of the stated theorem), as now you have multipliers everywhere. But the question seems interesting, if a touch vague.
Mar 8, 2012 at 18:04	comment	added	MTS		Can you give a bit more background? What do you mean by "algebraic quantum groups"? What prevents the proof of that theorem from going through naively?
Mar 8, 2012 at 15:04	history	asked	Fanf	CC BY-SA 3.0