Indecomposable representations of the nonlinear Lie algebras (Q2738286)

The two-state Heisenberg-Weyl algebra with usual creation and annihilation operators \(a_i^\pm\) (\(i=1,2\)) is considered. The representation of this algebra on its universal enveloping algebra \(\Omega\) is indecomposable. Nine different subalgebras \(R_{\lambda,\mu}\) (\(\lambda,\mu\in\{0,\pm 1\}\)) of this Heisenberg-Weyl algebra are considered. Each of these is a ``nonlinear Lie algebra'' with three basis elements. The rest of the paper is devoted to studying the indecomposable representations of \(R_{\lambda,\mu}\) on \(\Omega\).