In the theory of quantum groups Hopf algebras arise via the Fourier transform:(adsbygoogle = window.adsbygoogle || []).push({});

"A third point of view is that Hopf algebras are the next simplest category after Abelian groups admitting Fourier transform"

At least for nice functions, a Fourier series is just a Laurent series on a circle (which means just substituting [itex]z = re^{i\theta}[/itex] into a Laurent series), so I can see Fourier analysis on Abelian groups as generalizing this simple example.

How do I see (in an easy way) that Hopf Algebras are the natural generalization of Fourier theory to algebras, in a way that motivates what a Hopf algebra is, so that I have some feel for quantum groups?

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# Hopf Algebras in Quantum Groups

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