Quantum Dilogarithm Identities at Root of Unity
  We study the root of unity degeneration of cluster algebras and quantum dilogarithm identities. We prove identities for the cyclic dilogarithm associated with a mutation sequence of a quiver, and as a consequence new identities for the non-compact quantum dilogarithm at $b=1$. 
Ivan Chi-Ho Ip, Masahito Yamazaki
math.QA hep-th