Timeline for Recover Poisson bracket on $C[G]$ using the Lie cobracket $\delta: g \to \Lambda^2 g$

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Feb 13, 2016 at 15:52	comment	added	Alexander Chervov		@JianrongLi I guess you know that - if $\delta$ is coboundary it gives rise to $r$. The point is that in $r$-matrix notation corresponding bracket on $L^*$ will have the form $\{L \otimes L\} = [r , L\otimes 1 + 1 \otimes L ]$,
Feb 13, 2016 at 14:25	comment	added	Jianrong Li		thank you very much. I still have some questions. Using $\delta: L \to \Lambda^2 L$, we can obtain $[,]_{L^}: \Lambda^2 L^ \to L^*$. But how to compute the r-matrix $r$ for the Lie algebra $L$?
Feb 13, 2016 at 9:53	comment	added	Alexander Chervov		@JianrongLi The point is that they are the same $r = r^{Group}$ , the transformations which I made $r = 1 + \epsilon r $ they do not change the bracket, because RHS of bracket is given by commutator $[r, M \otimes M]$ so it exactly equals to $ [ (1+ r) , M \otimes M]$ because $1$ commute with everything. At least that how I remember things - I have not thought on these for years, it might be I misremember something, but the idea is like that.
Feb 13, 2016 at 2:32	comment	added	Jianrong Li		thank you very much. If we have a Lie cobracket $\delta: g \to \Lambda^2 g$, how to compute $r^{Group}$?
Feb 12, 2016 at 20:53	history	answered	Alexander Chervov	CC BY-SA 3.0