We initiate a new approach to maximal green sequences, whereby they are considered under an equivalence relation. Doing this reveals extra structure on the set of maximal green sequences of an algebra, namely hidden partial orders. We prove that there are several different ways of defining the equivalence relation. Similarly, there are several ways of defining a partial order on the equivalence classes, but as yet these partial orders are only conjecturally equivalent. We prove this conjecture in the case of Nakayama algebras.
This is joint work with Mikhail Gorsky.
This video was part of the Maurice Auslander International Conference.
