Study of formality for the Heisenberg algebra

Abstract

In this paper, we compute the Chevalley-Eilenberg cohomology of the three-dimensionnal Heisenberg Lie algebra with values in its universal enveloping algebra. We also compte the Schouten brackets on cochains and cohomology level in order to write the formality equations. It turns out that there is no formality, ans that the perturbed L-infinity structure on the cohomology has non-trivial terms in infinitely manu degrees.