Polyhedral Products, Graph Products, and $p$-Central Series

We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of graph products. As an 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.