The symmetry, period and Calabi–Yau dimension of finite dimensional mesh algebras

Within the class of finite dimensional mesh algebras, we identify those which are symmetric and those whose stable module category is Calabi–Yau. We also give, in combinatorial terms, explicit formulas for the Ω-period of any such algebra, where Ω is the syzygy functor, and for the Calabi–Yau Frobenius and the stable Calabi–Yau dimensions, when they are defined.