Hochschild cohomology of the algebra of conformal endomorphisms

Abstract

We prove that all Hochschild cohomology groups of the associative conformal algebra of conformal endomorphisms ${\mathrm{Cend}}_k$ with coefficients in an arbitrary conformal bimodule $M$ are trivial starting from the dimension 2, i.e., $H^n({\mathrm{Cend}}_k,M)=0$ for $n\ge 2$.