QUANTUM FRIEZE PATTERNS IN QUANTUM CLUSTER ALGEBRAS OF TYPE A

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International Electronic Journal of Algebra
Volume:12 Issue:12
QUANTUM FRIEZE PATTERNS IN QUANTUM CLUSTER ALGEBRAS OF TYPE A

QUANTUM FRIEZE PATTERNS IN QUANTUM CLUSTER ALGEBRAS OF TYPE A

Authors : Jeanphilippe BURELLE, Grégoire DUPONT

Pages : 103-115

View : 12 | Download : 9

Publication Date : 2012-12-01

Article Type : Research Paper

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.
Keywords : quantum cluster algebras, frieze patterns, continuant polynomials

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