Cluster algebras and derived categories

Understand

This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras.

• After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings admitting a cluster algebra structure.
• We then present the general definition of a cluster algebra and describe the interplay between cluster variables, coefficients, c-vectors and g-vectors.
• We show how c-vectors appear in the study of quantum cluster algebras and their links to the quantum dilogarithm.