Hochshild cohomology of the associative conformal algebra Cend_{1,x}

TL;DR

This paper proves that the second Hochschild cohomology group of the associative conformal algebra Cend_{1,x} is zero, implying certain splitting properties in algebra extensions.

Contribution

It establishes the vanishing of the second Hochschild cohomology for Cend_{1,x} and demonstrates its splitting behavior in extensions with nilpotent kernels.

Findings

Second Hochschild cohomology group of Cend_{1,x} is zero

Algebra splits off in extensions with nilpotent kernel

Provides insights into the structure of associative conformal algebras

Abstract

It is established in this work that second Hochshild cohomology group of the associative conformal algebra Cend_{1,x} is zero. As a corollary, this algebra split off in each extension with a nilpotent kernel. Key words: associative conformal algebra, splitting off radical, Hochshild cohomology.