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arXiv · 1207.3401

Monoidal categorifications of cluster algebras of type A and D

David Hernandez·Bernard Leclerc
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Abstract

In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and D, we show that these categories provide monoidal categorifications of cluster algebras of the same type. The proof is purely representation-theoretical, in the spirit of [arXiv:0903.1452].

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David Hernandez, Bernard Leclerc. 2012-07-14. Monoidal categorifications of cluster algebras of type A and D. https://arxiv.org/abs/1207.3401

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