Periodicities in cluster algebras and dilogarithm identities

Details Periodicities in cluster algebras and dilogarithm identities Periodicities in cluster algebras and dilogarithm identities

2010-06-03

arxiv.org/abs/1006.0632v5

Representations of algebras and related topics (A. Skowronski and K. Yamagata, eds.), EMS Series of Congress Reports, European

Mathematics

Quantum Algebra

37 pages, to appear in Representations of Algebras and Related Topics, Proceedings of ICRA XIV, Tokyo, 2010, title changed at

Scientific paper

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. We prove the identities when exchange matrices are skew symmetric.

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