We introduce the Virasoro algebra Vir as the universal central extension of the Witt algebra. This Lie algebra is a ℤ-graded Lie algebra and it is appropriate to work within the framework of what we call Q-graded Lie algebras. Hence, we also present a categorical setup for representations of Q-graded Lie algebras and some of their properties such as local composition series, (co)homologies, and Berstein-Gelfand-Gelfand duality.
KeywordsCentral Extension Free Abelian Group Verma Module High Weight Vector High Weight Module
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