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Pré-Publication, Document De Travail Année : 2012

Monoidal categorifications of cluster algebras of type A and D

David Hernandez
Bernard Leclerc

Résumé

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].

Dates et versions

hal-00797846 , version 1 (07-03-2013)

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David Hernandez, Bernard Leclerc. Monoidal categorifications of cluster algebras of type A and D. 2012. ⟨hal-00797846⟩
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