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arXiv · 1603.07958

Cohomology of vertex algebras

Jose I. Liberati
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Abstract

Let $V$ be a vertex algebra and $M$ a $V$-module. We define the first and second cohomology of $V$ with coefficients in $M$, and we show that the second cohomology $H^{2}(V, M)$ corresponds bijectively to the set of equivalence classes of square-zero extensions of $V$ by $M$. In the case that $M=V$, we show that the second cohomology $H^{2}(V, V)$ corresponds bijectively to the set of equivalence classes of first order deformations of $V$.

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Jose I. Liberati. 2016-03-25. Cohomology of vertex algebras. https://arxiv.org/abs/1603.07958

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