E_n-cohomology with coefficients as functor cohomology

TL;DR

This paper demonstrates that E_n-cohomology with coefficients in a symmetric bimodule can be understood as functor cohomology, and shows that the related Yoneda algebra is trivial, extending previous work by Livernet and Richter.

Contribution

It establishes a functor cohomology interpretation of E_n-cohomology with coefficients and proves the triviality of the associated Yoneda algebra, building on Livernet and Richter's work.

Findings

E_n-cohomology with coefficients as functor cohomology

Yoneda algebra associated with E_n-cohomology is trivial

Extension of Livernet and Richter's results

Abstract

Building on work of Livernet and Richter, we prove that E_n-homology and E_n-cohomology of a commutative algebra with coefficients in a symmetric bimodule can be interpreted as functor homology and cohomology. Furthermore we show that the associated Yoneda algebra is trivial.