This talk will begin by constructing a new algebra based on a generalization of the set of relations for Ozsváth-Szabó’s bordered Heegaard Floer algebra $B(n,k)$. Then, I will strengthen an existing result by establishing an isomorphism between our new algebra and the algebra $\widetilde{B}(\mathcal{V})$ associated with an arrangement of real affine hyperplanes. If time permits, I’ll introduce a differentially graded algebra, $\widetilde{B}(\mathcal{V},S)$, and discuss ongoing work including finding its appropriate Koszul dual and understanding its homology and formality conditions.