Periodic actions on distributive lattices and counterparts in algebra

Let L be a distributive lattice and A be its incidence algebra. There is a celebrated combinatorial action on posets called “rowmotion”. Thanks to a result of Iyama-Marczinzik, we can think of this combinatorial action as the grade bijection defined on the algebra A. On the other hand, the Coxeter transformation plays an important role in representation theory of algebras and in some cases it shows some periodicity. The periodicity of the Coxeter transformation is motivated by the fractionally Calabi-Yau property of a certain category. Motivated by these, we show that the composition of the rowmotion and the Coxeter transformation is periodic for the algebra A in a joint work with René Marczinzik and Hugh Thomas.