On quantum cluster algebras of finite type

Ming Ding

doi:10.1007/s11464-011-0104-2

Front. Math. China ›› 2011, Vol. 6 ›› Issue (2) : 231 -240. DOI: 10.1007/s11464-011-0104-2

Research Article

RESEARCH ARTICLE

On quantum cluster algebras of finite type

Ming Ding ¹^,^a

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Abstract

We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra [inline-graphic not available: see fulltext](Q) generated by all cluster characters is exactly the quantum cluster algebra [inline-graphic not available: see fulltext](Q).

Keywords

Cluster variable / quantum cluster algebra

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Ming Ding. On quantum cluster algebras of finite type. Front. Math. China, 2011, 6(2): 231-240 DOI:10.1007/s11464-011-0104-2

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