Nikita Markarian’s mathblog

Classifying operad

Posted in Mathematics by nikitamarkarian on June 5, 2009

In the previous post everything is based on the following observation. Let A be an algebra over chains of small discs operad. Then A is in particular a homotopy algebra. I propose that on Hochschild homology of A there is a natural action of an operad equivalent to the
associative operad Ass (this is essentially proved in M. Brun, Z. Fiedorowicz, R. Vogt “On the multiplicative structure of topological Hochschild homology”). More generally, one may try introduce of action (whatever it means) of an operad equivalent to Ass on the category of twisted (semifree) complexes of A and derive the previous action from this one.

Thinking about a proof of this statement I formulated a more general question.