We consider GL _m -dimers of triangulations of regular convex n-gons, which give rise to a dimer model with boundary Q and a dimer algebra Λ _Q . Let e_b be the sum of the idempotents of all the boundary vertices, and $B_Q:=e_b{\Lambda }_Q{e}_b$ the associated boundary algebra. In this article we show that given two different triangulations T ₁ and T ₂ of the n-gon, the boundary algebras are isomorphic, i.e. $e_b{\Lambda }_{Q_{T_1}}{e}_b\cong e_b{\Lambda }_{Q_{T_2}}{e}_b.$

Keywords: 16G20; 57Q15; 82B20; Boundary algebra; dimer model; quiver; triangulation.

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