Cohomology of vertex algebras

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 $V$.

arXiv comment11 pages. arXiv admin note: text overlap with arXiv:1008.2351 by other authors