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Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra (1011.3438v6)
Published 15 Nov 2010 in math.RT, math-ph, math.MP, math.QA, and math.RA
Abstract: In this paper, we provide a uniform method to thoroughly classify all Harish-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 some Lie algebras and superconformal algebras related to the Virasoro algebra, including the several kinds of Schr\"odinger-Virasoro Lie algebras, which are open up to now.