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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Testing isomorphism of graded algebras
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by Peter A. Brooksbank, E. A. O’Brien and James B. Wilson PDF
Trans. Amer. Math. Soc. 372 (2019), 8067-8090 Request permission


We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.
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Additional Information
  • Peter A. Brooksbank
  • Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
  • MR Author ID: 321878
  • E. A. O’Brien
  • Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
  • MR Author ID: 251889
  • James B. Wilson
  • Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
  • MR Author ID: 881789
  • Received by editor(s): July 24, 2017
  • Received by editor(s) in revised form: March 6, 2019
  • Published electronically: August 1, 2019
  • Additional Notes: This work was supported in part by the Marsden Fund of New Zealand via grant UOA 1626, by NSF grants DMS-1620454 and DMS-1620362, and by the Simons Foundation $\#$281435.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 8067-8090
  • MSC (2010): Primary 17-08, 15A69, 68Q25; Secondary 20D15, 17B70
  • DOI:
  • MathSciNet review: 4029690