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Warning!
Dear Colleague, I have found an important typo in Equation (4.5) of the printed version of this work. This formula is key to present Drinfeld doubles by generators and relations. I use this presentation to study the representation theory of Drinfeld doubles.
So, I upload a new version of this paper in arxiv. By correcting it, I also realised that this equation can be written
in a nicer form. Explicitly, Equation (4.5) now reads
\([\!\!\![y,x]\!\!\!]:=yx-(y_{(-1)}\cdot x)y_{(0)}-\langle y,x\rangle+y_{(-1)}x_{(-1)}\langle y_{(0)},x_{(0)}\rangle\)
and the old and correct formula was
\([\!\!\![y,x]\!\!\!]:=yx-(y_{(-1)}\cdot x)y_{(0)}-\langle y,x\rangle+\langle y_{(-2)},x_{(-3)}\rangle\langle y_{(0)},\mathcal{S}(x_{(-1)})\cdot x_{(0)}\rangle\, x_{(-2)}y_{(-1)}\).
The typo consisted of flipping \(y_{(-1)}\) and \(x_{(-2)}\) in the last summand. I prove that both formulas are equals in this
file.
Having said these words of caution, the printed version is in this
link
and the new arxiv version is
here.