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arXiv · 1706.04376

Cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$

Liqian Bai·Xueqing Chen·Ming Ding·Fan Xu
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Abstract

The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases established in [6], and naturally deduce the positivity of the elements in these bases. One bar-invariant basis as the triangular basis of this quantum cluster algebra is also explicitly described.

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Liqian Bai, Xueqing Chen, Ming Ding, Fan Xu. 2017-06-14. Cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. https://arxiv.org/abs/1706.04376

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