Denominators in cluster algebras of affine type

Details Denominators in cluster algebras of affine type Denominators in cluster algebras of affine type

2008-05-04

arxiv.org/abs/0805.0439v1

Mathematics

Representation Theory

21 pages

Scientific paper

The Fomin-Zelevinsky Laurent phenomenon states that every cluster variable in a cluster algebra can be expressed as a Laurent polynomial in the variables lying in an arbitrary initial cluster. We give representation-theoretic formulas for the denominators of cluster variables in cluster algebras of affine type. The formulas are in terms of the dimensions of spaces of homomorphisms in the corresponding cluster category, and hold for any choice of initial cluster.

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