Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and F-polynomials

Min Huang Zhejiang University Fang Li Zhejiang University

Representation Theory mathscidoc:1702.30004

arXiv:1609.05981v2 [math.RT], 48, 2016.11
In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in [6] which asks whether an acyclic signskew- symmetric matrix is always totally sign-skew-symmetric. As applications, the positivity for cluster algebras in acyclic sign-skew-symmetric case is given; further, the F-polynomials of cluster algebras are proved to have constant term 1 in acyclic sign-skew-symmetric case.
cluster algebra; sign-skew-symmetric matrix; unfolding method; positivity conjecture; F-polynomial
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@inproceedings{min2016unfolding,
  title={Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and F-polynomials},
  author={Min Huang, and Fang Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170221221938829392482},
  booktitle={arXiv:1609.05981v2 [math.RT]},
  pages={48},
  year={2016},
}
Min Huang, and Fang Li. Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and F-polynomials. 2016. In arXiv:1609.05981v2 [math.RT]. pp.48. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170221221938829392482.
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