Positivity in skew-symmetric cluster algebras of finite type

Details Positivity in skew-symmetric cluster algebras of finite type Positivity in skew-symmetric cluster algebras of finite type

2011-02-15

arxiv.org/abs/1102.3050v2

Mathematics

Rings and Algebras

12 pages, small changes, I added remark 5.1

Scientific paper

We prove that the basis of cluster monomials of a skew-symmetric cluster
algebra A of finite type is the atomic basis of A. This means that an element
of A is positive if and only if it has a non-negative expansion in the basis of
cluster monomials. In particular cluster monomials are positive indecomposable,
i.e. they cannot be written as a sum of positive elements.

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