Every ribbon graph order has a Nakayama automorphism making it twisted 1-Calabi-Yau, and it is symmetric, hence 1-Calabi-Yau, precisely when the ribbon graph is bipartite or the field has characteristic two.
On Jacobian algebras from closed surfaces
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abstract
We show that the quivers with potentials associated to ideal triangulations of marked surfaces with empty boundary are not rigid, and their completed Jacobian algebras are finite-dimensional and symmetric.
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Calabi-Yau properties of ribbon graph orders
Every ribbon graph order has a Nakayama automorphism making it twisted 1-Calabi-Yau, and it is symmetric, hence 1-Calabi-Yau, precisely when the ribbon graph is bipartite or the field has characteristic two.