Quantum frieze patterns in quantum cluster algebras of type A

2012/02/09 by Jean-Philippe Burelle, Burelle, Jean-Philippe, Grégoire Dupont +1
Mathematics · #05E15 #13F60 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.CO #math.QA #math.RA #msc:05E15 #msc:13F60

paper · pdf · doi:10.48550/arxiv.1202.1906

10 pages

arxiv created 2012/02/09 · arxiv updated 2012/02/10

Abstract

We introduce a quantisation of the Coxeter-Conway frieze patterns and prove that they realise quantum cluster variables in quantum cluster algebras associated with linearly oriented Dynkin quivers of type A. As an application, we obtain the explicit polynomials arising from the lower bound phenomenon in these quantum cluster algebras.

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