On cluster theory and quantum dilogarithm identities

2011/02/21 by Keller, Bernhard · 5 citations
#14N35 #16G20 (Primary) 18E30 (Secondary) 17B37 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1102.4148

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.

Cited by

• Classical tilting and τ-tilting theory via duplicated algebras
• Reddening sequences and mutation of infinite quivers
• Integral cluster structures on quantized coordinate rings
• Oriented matroids from type \mathbbA cluster categories
• An introduction to representation-theoretic canonical bases of cluster algebras

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