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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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Affine zigzag algebras and imaginary strata for KLR algebras
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by Alexander Kleshchev and Robert Muth PDF
Trans. Amer. Math. Soc. 371 (2019), 4535-4583 Request permission

Abstract:

KLR algebras of affine $\texttt {ADE}$ types are known to be properly stratified if the characteristic of the ground field is greater than some explicit bound. Understanding the strata of this stratification reduces to semicuspidal cases, which split into real and imaginary subcases. Real semicuspidal strata are well understood. We show that the smallest imaginary stratum is Morita equivalent to Huerfano-Khovanov’s zigzag algebra tensored with a polynomial algebra in one variable. We introduce affine zigzag algebras and prove that these are Morita equivalent to arbitrary imaginary strata if the characteristic of the ground field is greater than the bound mentioned above.
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Additional Information
  • Alexander Kleshchev
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • MR Author ID: 268538
  • Email: klesh@uoregon.edu
  • Robert Muth
  • Affiliation: Department of Mathematics, Washington and Jefferson College, Washington, Pennsylvania 15301
  • MR Author ID: 1191042
  • Email: rmuth@washjeff.edu
  • Received by editor(s): January 20, 2016
  • Received by editor(s) in revised form: June 19, 2017
  • Published electronically: September 13, 2018
  • Additional Notes: The first author was supported by the NSF grant DMS-1161094, Max-Planck-Institut, and the Fulbright Foundation.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 4535-4583
  • MSC (2010): Primary 20C08, 17B10, 05E10
  • DOI: https://doi.org/10.1090/tran/7464
  • MathSciNet review: 3934461