Abstract:
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.
Citation:
Kyungyong Lee, Li Li, Matthew R. Mills, “A Combinatorial Formula for Certain Elements of Upper Cluster Algebras”, SIGMA, 11 (2015), 049, 24 pp.
\Bibitem{LeeLiMil15}
\by Kyungyong~Lee, Li~Li, Matthew~R.~Mills
\paper A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
\jour SIGMA
\yr 2015
\vol 11
\papernumber 049
\totalpages 24
\mathnet{http://mi.mathnet.ru/sigma1030}
\crossref{https://doi.org/10.3842/SIGMA.2015.049}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3360733}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000356976600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84934784184}
Linking options:
https://www.mathnet.ru/eng/sigma1030
https://www.mathnet.ru/eng/sigma/v11/p49
This publication is cited in the following 4 articles:
Liqian Bai, Xueqing Chen, Ming Ding, Fan Xu, “On the Generalized Cluster Algebras of Geometric Type”, SIGMA, 16 (2020), 092, 14 pp.
J. W. Lawson, M. R. Mills, “Properties of minimal mutation-infinite quivers”, J. Comb. Theory Ser. A, 155 (2018), 122–156
M. Huang, F. Li, “Unfolding of sign-skew-symmetric cluster algebras and its applications to positivity and F-polynomials”, Adv. Math., 340 (2018), 221–283
K. Lee, L. Li, B. Nguyen, “New combinatorial formulas for cluster monomials of type A quivers”, Electron. J. Comb., 24:2 (2017), P2.42
Citation in format AMSBIB
Contact us: