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

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

2010-11-15

arxiv.org/abs/1011.3438v4

Mathematics

Representation Theory

Latex, 22 pages

Scientific paper

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\"{o}dinger-Virasoro Lie algebras, which are open up to now.

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