2017/06/27 by Pasquali, Andrea
#05E15 (Secondary) #13F60 #16G10 (Primary) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1706.08756
We study a finite-dimensional algebra Λ constructed from a Postnikov diagram D in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent. Thus Λ is isomorphic to the stable endomorphism algebra of the cluster tilting module T∈\underlineCM(B) introduced by Jensen-King-Su in order to categorify the cluster algebra structure of \mathbb C[Grk(\mathbb Cn)]. We show that Λ is self-injective if and only if D has a certain rotational symmetry. In this case, Λ is the Jacobian algebra of a self-injective quiver with potential, which implies that its truncated Jacobian algebras in the sense of Herschend-Iyama are 2-representation finite. We study cuts and mutations of such quivers with potential leading to some new 2-representation finite algebras.