The polyhedral product functor over a simplicial complex $K$ can be defined in a category with finite products and colimits. For the category of groups, it depends only on the one-skeleton of $K$ and is known as the graph product. This categorical framework allows one to relate several results on loop homology of polyhedral products with graph products of groups, their central series and associated Lie algebras. By way of application, we describe the restricted Lie algebra associated with the lower 2-central series of a right-angled Coxeter group and identify its universal enveloping algebra with the loop homology of the Davis-Januszkiewicz space.

This is a joint work with Temurbek Rahmatullaev.