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We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $T$. Let $mathfrak{h}=C L_0oplusC G_0$ be the Cartan subalgebra of $T$, and let $mathfrak{t}=C L_0$ be the Cartan subalgebra of even part $T_{bar 0}$. These modules over $T$ when restricted to the $mathfrak{h}$ are free of rank $1$ or when restricted to the $mathfrak{t}$ are free of rank $2$. We provide the sufficient and necessary conditions for those modules being simple, as well as giving the sufficient and necessary conditions for two $T$-modules being isomorphic. We also compute the action of an automorphism on them. Moreover, based on the weighting functor introduced in cite{N2}, a class of intermediate series modules $A_sigma$ are obtained. As a byproduct, we give a sufficient condition for two $T$-modules are not isomorphic.
In the present paper, using the technique of localization, we determine the center of the quantum Schr{o}dinger algebra $S_q$ and classify simple modules with finite-dimensional weight spaces over $S_q$, when $q$ is not a root of unity. It turns out
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In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.