I couldn't find a list of open problems in Hopf algebras. So my question is the following:
In the theory of Hopf algebras, what are the (big) open problems?
Any kind of problem/question will be welcome. I am interested in any kind of problem involving Hopf algebras, say going from combinatorics or topology to abstract algebra.
Best Answer
There had been a workshop on Hopf algebras and related areas in September 2015. Its report (https://www.birs.ca/workshops//2015/15w5053/report15w5053.pdf) includes a large list of open problems and conjectures in Hopf algenbras, for example "Is the antipode of a noetherian Hopf algebra bijective ?".