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A few weeks ago I had a very engaging talk with a faculty member, where he told me lots of interesting things about quantum algebras, know theory and Reshetikhin-Turaev invariants (this field is not my domain of of expertise).

Among other things he searched on the internet for an introductory book for this field and we browsed through a few ones, until he found one that he mentioned might be interesting to me.

Because I received so much information, I wasn't able to remember the name of that book! I searched in vain for keywords like "quantum groups", "quantum algebras", "TQFT".

I only remember that:

  • the book had 2 (or more) Russian authors
  • in the first ~100 pages it developed a lot of abstract category-theoretic machinery, before it turned to more concrete things (to the point that said faculty member wondered whether that was actually necessary in order to understand the concrete stuff)
  • it had a cover that looked similar to this or like this in terms of color and layout
  • it came up on the right-hand side of the browser in Google (not Google books) when searching for it, so it must be frequently searched-for book
  • It contains some knot theory as well

Could you please help me find that book? I hope all of these contraints will hopefully uniquely identify it.

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    $\begingroup$ Is there some reason you can't ask the faculty member? $\endgroup$
    – LSpice
    Aug 6, 2019 at 13:34
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    $\begingroup$ Quantum Invariants of Knots and 3-Manifolds has the right color but only one Russian author, Turaev. $\endgroup$ Aug 6, 2019 at 13:40
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    $\begingroup$ Tensor Categories seems to roughly match your description, but I suspect it is not unique in that regard. $\endgroup$ Aug 6, 2019 at 13:42
  • $\begingroup$ As you mention "might be interesting to me" perhaps it would be helpful to know about your area of expertise, background, and interests. In general, Tensor Categories is self contained and would certainly be a good starting point, as would books like Kassel's "Quantum Groups," Turaev's previously mentioned book, Bakalov and Kirilov's "Tensor Categories and Modular Functors," Zhenghan Wang's "Topological Quantum Computing." So much of what would be good and direct answering this question is dependent upon what part of the conversation had you going "Wow! That's cool!" $\endgroup$ Aug 6, 2019 at 17:32
  • $\begingroup$ @LSpice Yes, there is, but I can't share it here. $\endgroup$
    – user43263
    Aug 7, 2019 at 14:54

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