I am currently reading the paper "Calabi-Yau Algebras and Superpotential" by Van Den Bergh, but I find it highly confusing. In Section 10 he mention that bracket {$-,-$}$\space_{\omega_\eta}$ becomes the necklace Lie bracket. How is this defined in the following setting:
Let $T_D(S)$ be a tensor algebra of a species $S=(D, M)$, where $D$ is sum of divisions rings and $M$ a $D-D-$bimodule and choose a potential
$$ W\in T_D(S)/[T_D(S), T_D(S)]. $$
How is the necklace Lie bracket {$W, -$} defined here?
In the quiver case it becomes the cyclic derivation of the potential, and I would guess that in the species case it should be something similar.