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In this paper, we provide a uniform method to thoroughly classify allHarish-Chandra modules over some Lie algebras related to the Virasoro algebras.We first classify such modules over the Lie algebra $W(\varrho)[s]$ for$s=0,\frac12$. With this result and method, we can also do such works for someLie algebras and superconformal algebras related to the Virasoro algebra,including the several kinds of Schr\"odinger-Virasoro Lie algebras, which areopen up to now.

Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra