Algebraic structures in Lagrangian Floer cohomology modelled on differential forms

We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is constructed in the differential forms model. In the spirit of Ganatra and Hugtenburg, we define another such algebra structure using a closed-open map. We show that the two structures coincide. As an application, we show that the module structure for the 2-dimensional Clifford torus is given by multiplication by a Novikov coefficient, similarly to the Biran-Cornea module structure for this case.