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Let $\mathfrak{h}_{2n}$ be the Heisenberg Lie algebra, i.e. the Lie algebra with a basis of $\{p_1,\ldots,p_n,q_1,\ldots,q_n,c\}$ where $$[Pi, Pj ] = [Qi, Qj ] = [Pi, C] = [Qi, C] = [C, C] = 0, [Pi, Qj ] = Cδ_{ij}$$ for all $i,j \in \{1,\ldots,n\}$. I know that you can use the PBW theorem to show that the universal envelloping algebra $U(\mathfrak{h}_{2n})$ is a quotient of the Weyl algebra $W_n$ (see http://en.wikipedia.org/wiki/Heisenberg_group).

Can I use this to find the centre of $U(\mathfrak{h}_{2n})$? If not, how can one find the centre of $U(\mathfrak{h}_{2n})$?

Thanks.

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