Cluster Scattering Diagrams and Theta Functions for Reciprocal Generalized Cluster Algebras

Dilogarithm Identities in Cluster Scattering Diagrams

“…(iii) = 3. The relation (5.2) is reduced at = 3 to 0 1 (5.12) Thus, the reduced DI at = 3 is L(y 2 + 2y 1 y 2 + y 2 1 y 2 ) + L(y 1 ) ≡ L(y 1 − 2y 1 y 2 − 4y 2 1 y 2 + 3y 1 y 2 2 ) + L(y 2 1 y 2 ) + 2 L(y 1 y 2 − 2y 1 y 2 2 ) + L(y 1 y 2…”

“… The y -variables are also known as cluster -variables [7]. The corresponding theta functions were studied via the CSDs with principal coefficients in [14] and via the scattering diagrams with the Langlands dual data ( scattering diagrams) in [2], [3]. Apparently, our y -variables in CSDs are defined in a different way, and we do not know how they are related to the ones in the above works.…”