On cluster theory and quantum dilogarithm identities
Representation Theory
2011-10-14 v4 Combinatorics
Quantum Algebra
Abstract
These are expanded notes from three survey lectures given at the 14th International Conference on Representations of Algebras (ICRA XIV) held in Tokyo in August 2010. We first study identities between products of quantum dilogarithm series associated with Dynkin quivers following Reineke. We then examine similar identities for quivers with potential and link them to Fomin-Zelevinsky's theory of cluster algebras. Here we mainly follow ideas due to Bridgeland, Fock-Goncharov, Kontsevich-Soibelman and Nagao.
Keywords
Cite
@article{arxiv.1102.4148,
title = {On cluster theory and quantum dilogarithm identities},
author = {Bernhard Keller},
journal= {arXiv preprint arXiv:1102.4148},
year = {2011}
}
Comments
32 pages, 5 figures; v2: reference added; v3: section 4.5 corrected, references updated; v4: end of section 1.7 corrected