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arXiv · 1405.2311

Greedy bases in rank 2 quantum cluster algebras

Kyungyong Lee·Li Li·Dylan Rupel·Andrei Zelevinsky
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Abstract

We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky.

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Kyungyong Lee, Li Li, Dylan Rupel, Andrei Zelevinsky. 2014-05-09. Greedy bases in rank 2 quantum cluster algebras. https://doi.org/10.1073/pnas.1313078111

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