Ozsváth-Szabó bordered algebras and subquotients of category \(\mathcal{O} \) (Q2214096)

In the paper under review it is proved that for \(0\leq k\leq n\), Ozsváth-Szabó's algebra \(B_l(n,k)\) is a graded flat deformation of Sartori's algebra \(A_{n,k}\). The projection functors between categories of finitely generated projective graded modules over these algebras induce isomorphisms on Grothendieck groups \(K_0\) intertwining the identification of indecomposable projectives with canonical basis elements on each side. The constructed isomorphism allows to transport a number of other constructions between these two algebras.