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Bar-invariant bases of the quantum cluster algebra of type A (2)2

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Abstract

We construct bar-invariant ℤ[q ±1/2]-bases of the quantum cluster algebra of the valued quiver A (2)2 , one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, University of Wisconsin-Whitewater, 800 W. Main Street, Whitewater, WI, 53190, USA

    Xueqing Chen

  2. Center for Advanced Study, Tsinghua University, Beijing, 10084, P.R.China

    Ming Ding

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R.China

    Jie Sheng

Authors
  1. Xueqing Chen
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  2. Ming Ding
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  3. Jie Sheng
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Correspondence to Xueqing Chen.

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Cordially dedicated to Prof. Vlastimil Dlab on the occasion of his 80th birthday

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Chen, X., Ding, M. & Sheng, J. Bar-invariant bases of the quantum cluster algebra of type A (2)2 . Czech Math J 61, 1077–1090 (2011). https://doi.org/10.1007/s10587-011-0049-3

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  • DOI: https://doi.org/10.1007/s10587-011-0049-3

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