Second cohomology group of extended W-algebras

Abstract

Let $\mathbb{F}$ be a field of characteristic 0, and let G be an additive subgroup of $\mathbb{F}$. We define a class of infinite-dimensional Lie algebras [inline-graphic not available: see fulltext] with an $\mathbb{F}$-basis {L _µ, V _µ, W _µ | µ ∈ G}, which are very closely related to W-algebras. In this paper, the second cohomology group of [inline-graphic not available: see fulltext] is determined.

Keywords

W-algebra / second cohomology group / central extension

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