I'm interested in learning about quantum groups about a $C^*$-algebraic perspective.

I'm familiar with (the basics) of topology, abstract algebra, measure theory, functional analysis (in particular $C^*$-algebras) and category theory.

However I don't know much about related topics like Hopf-algebras etc.

What references can you recommend and in what order should I read them?



If you have never seen anything about Hopf algebras I recommend perhaps looking at Section 2.2 of my own thesis. It is a very leisurely introduction in the technically easy finite dimensional case.

Perhaps for a first look at $\mathrm{C}^*$-algebraic quantum groups these notes of Roland Vergnioux might be a good idea:

These notes really well-motivate the definition and relate the definition very well to the commutative situation.

An overarching reference might be: - Thomas Timmermann, An Invitation to Quantum Groups and Duality - From Hopf Algebras to Multiplicative Unitaries and Beyond

However perhaps use this as a reference and instead look at graduate lecture notes such as (in no particular order):

Between these you are in good nick.

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  • $\begingroup$ Thanks! This will definitely help! $\endgroup$ – user745578 May 10 at 15:28
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    $\begingroup$ @user745578 I wouldn't be shy of reading papers either, especially older papers of Woronowicz and Van Daele. Personally I really like the (old) paper of Kac and Paljutkin but again that is from the finite pov. $\endgroup$ – JP McCarthy May 10 at 16:08
  • $\begingroup$ Don't you think those papers are a little too advanced to start with? $\endgroup$ – user745578 May 10 at 19:43
  • $\begingroup$ @user745578 I didn't say to start with those papers. $\endgroup$ – JP McCarthy May 10 at 22:12
  • $\begingroup$ @user745578 ooooh this is nice: math.uni-sb.de/ag/speicher/weber/… $\endgroup$ – JP McCarthy May 11 at 6:31

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