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Transactions of the American Mathematical Society

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

 
 

 

Testing isomorphism of graded algebras


Authors: Peter A. Brooksbank, E. A. O’Brien and James B. Wilson
Journal: Trans. Amer. Math. Soc. 372 (2019), 8067-8090
MSC (2010): Primary 17-08, 15A69, 68Q25; Secondary 20D15, 17B70
DOI: https://doi.org/10.1090/tran/7884
Published electronically: August 1, 2019
MathSciNet review: 4029690
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.
Article copyright: © Copyright 2019 American Mathematical Society