Laurent expansions in cluster algebras via quiver representations

Details Laurent expansions in cluster algebras via quiver representations Laurent expansions in cluster algebras via quiver representations

2006-04-04

arxiv.org/abs/math/0604054v4

Mathematics

Representation Theory

19 pages; v2: added Remark 5.7; v3: minor editorial changes, final version to appear in Moscow Math. Journal; v4: more minor e

Scientific paper

We study Laurent expansions of cluster variables in a cluster algebra of rank
2 associated to a generalized Kronecker quiver. In the case of the ordinary
Kronecker quiver, we obtain explicit expressions for Laurent expansions of the
elements of the canonical basis for the corresponding cluster algebra.

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