On extensions of Lie algebras by means of the Heisenberg algebra (Q2508737)

Let \(H_n\) be a \((2n+1)\)-dimensional Heisenberg algebra, let \(G\) be a Lie algebra and let \(E(G,H_n)\) be the set of Lie algebras, which are extensions of \(G\) by \(H_n\). The author proves that the algebras in \(E(G,H_n)\) are in one-to-one correspondence with the pairs \((\rho,\omega)\), where \(\rho:G\mapsto \widehat{sp}(H_n/Z(H_n))\) is a representation of \(G\), \(\omega\in H^2(G,Z(H_n))\), and \(Z(H_n)\) is the center of \(H_n\).