Periodicities in cluster algebras and dilogarithm identities

Understand

We consider two kinds of periodicities of mutations in cluster algebras.

• For any sequence of mutations under which exchange matrices are periodic, we define the associated T- and Y-systems.
• When the sequence is `regular', they are particularly natural generalizations of the known `classic' T- and Y-systems.
• Furthermore, for any sequence of mutations under which seeds are periodic, we formulate the associated dilogarithm identity.