I'm looking for reasons that motivate the study of Hopf Algebra, like its applications in other branches of mathematics or maybe with physics. The first I've got is that they're interesting by themselves. But I'll want to motivate the undergaduate students and I'll like give them a vast vision of the matter.
Why study Hopf Algebras?
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education
quantum-groups
noncommutative-geometry
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5While somewhat jokingly, this is also a question I would normally reply when people ask me why study things as set theory: **Why not??** – 2011-10-25
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4Nothing will be a more convincing motivation that a description of why *you* are trying to have them study Hopf algebras. It is somewhat weak to give other people's motivations (that someone somewhere uses Hopf algebras to systematize the regularization process for Feynman integrals when they are not going to be doing that any time soon is not too exciting) – 2011-10-25
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6@Mariano: While I agree that the teacher should have some motivation of their own, I disagree that other people's motivations are useless for teaching. I feel that it is one of the most important aspect of a lecture to point out links. Obviously, it will not be very useful if the link is to things one does not understand at all, but there may be examples that actually *remind* one of things one has already seen. – 2011-10-25
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1One cool application of Hopf algebras is to prove that: The de-Rham cohomology of a Lie Group is an exterior algebra on odd degree generators. – 2018-09-10