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{\LARGE{\bf Cheat Sheet Quantum Groups}\quad\footnotesize Every Formula Worth Dreading}\hfill
\parbox[b]{2.5in}{\tiny
  \null\hfill\url{http://drorbn.net/AcademicPensieve/2017-02/}
  \newline\null\hfill
   continues \href{http://drorbn.net/AcademicPensieve/2016-10/}{2016-10}, modified \today,
   continued \href{http://drorbn.net/AcademicPensieve/2017-03/}{2017-03}
}

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\cite[Example~1.3.2]{Majid:Foundations}. A Hopf algebra over $\bbQ[q^{\pm 1}]$:
\[ \langle 1, X, g^{\pm 1}\rangle\left/\left(Xg^{\pm 1}=q^{\pm 1}g^{\pm 1}X\right)\right., \]
with
$\Delta\colon(X,\,g^{\pm 1})\mapsto(X\otimes 1+g\otimes X,\ g^{\pm 1}\otimes g^{\pm 1})$,
$\epsilon\colon(X,\,g^{\pm 1})\mapsto (0,\,1)$,
and $S\colon(X,\,g^{\pm 1})\mapsto (-g^{-1}X,\,g^{\mp 1})$. Has $S^2\neq 1$.

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\cite[Example 18.8]{Majid:Primer} (seems to have no universal $R$ formula):\newline
\includegraphics[width=\linewidth]{Majid-Primer-118.png}

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\cite[Theorem~8.3.9]{ChariPressley}:\newline
\includegraphics[width=\linewidth]{ChariPressley-273.png}

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\bibitem[CP]{ChariPressley} V.~Chari and A.~Pressley,
  {\em A Guide to Quantum Groups,}
  Cambridge University Press, 1994.

\bibitem[Ka]{Kassel} C.~Kassel,
  {\em Quantum groups,}
  Springer-Verlag GTM {\bf 155}, Heidelberg 1994.

\bibitem[Ma1]{Majid:Foundations} S.~Majid,
  {\em Foundations of Quantum Group Theory,}
  Cambridge University Press, 1995.

\bibitem[Ma2]{Majid:Primer} S.~Majid,
  {\em A Quantum Groups Primer,}
  London Mathematical Society Lecture Note Series {\bf 292}, Cambridge University Press, 2002.

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