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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quantum cluster characters for valued quivers
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by Dylan Rupel PDF
Trans. Amer. Math. Soc. 367 (2015), 7061-7102 Request permission

Abstract:

Let $\mathbb {F}$ be a finite field and $(Q,\mathbf {d})$ an acyclic valued quiver with associated exchange matrix $\tilde {B}$. We follow Hubery’s approach to prove our main conjecture from 2011: the quantum cluster character gives a bijection from the isoclasses of indecomposable rigid valued representations of $Q$ to the set of non-initial quantum cluster variables for the quantum cluster algebra $\mathcal {A}_{|\mathbb {F}|}(\tilde {B},\Lambda )$. As a corollary we find that for any rigid valued representation $V$ of $Q$, all Grassmannians of subrepresentations $Gr_{\mathbf {e}}^V$ have counting polynomials.
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Additional Information
  • Dylan Rupel
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • Address at time of publication: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
  • Email: drupel@uoregon.edu, d.rupel@neu.edu
  • Received by editor(s): August 29, 2012
  • Received by editor(s) in revised form: July 24, 2013
  • Published electronically: March 2, 2015
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7061-7102
  • MSC (2010): Primary 16G20, 16T99; Secondary 16G70, 16S38
  • DOI: https://doi.org/10.1090/S0002-9947-2015-06251-5
  • MathSciNet review: 3378824