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arXiv · 1412.8106

Monoidal categorification of cluster algebras

Seok-Jin Kang·Masaki Kashiwara·Myungho Kim·Se-jin Oh
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Abstract

We give a definition of monoidal categorifications of quantum cluster algebras and provide a criterion for a monoidal category of finite-dimensional graded $R$-modules to become a monoidal categorification of a quantum cluster algebra, where $R$ is a symmetric Khovanov-Lauda-Rouquier algebra. Roughly speaking, this criterion asserts that a quantum monoidal seed can be mutated successively in all the directions once the first-step mutations are possible. In the course of the study, we also give a proof of a conjecture of Leclerc on the product of upper global basis elements.

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Seok-Jin Kang, Masaki Kashiwara, Myungho Kim, Se-jin Oh. 2014-12-28. Monoidal categorification of cluster algebras. https://arxiv.org/abs/1412.8106

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