  The dilogarithm identities for the central charges of conformal field
theories of simply laced type were conjectured by Bazhanov, Kirillov, and
Reshetikhin. Their functional generalizations were conjectured by Gliozzi and
Tateo. They have been partly proved by various authors. We prove these
identities in full generality for any pair of Dynkin diagrams of simply laced
type based on the cluster algebra formulation of the Y-systems.
