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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
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by T. H. Lenagan and Agata Smoktunowicz PDF
J. Amer. Math. Soc. 20 (2007), 989-1001 Request permission

Abstract:

The famous 1960’s construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not locally nilpotent, algebra which has polynomially bounded growth.
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Additional Information
  • T. H. Lenagan
  • Affiliation: Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
  • MR Author ID: 189331
  • Email: tom@maths.ed.ac.uk
  • Agata Smoktunowicz
  • Affiliation: Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956 Warsaw 10, Poland
  • Address at time of publication: Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
  • MR Author ID: 367000
  • Email: agatasm@impan.gov.pl
  • Received by editor(s): May 25, 2005
  • Published electronically: April 2, 2007
  • Additional Notes: The first author acknowledges support by Leverhulme Grant F/00158/X
    Part of this work was done while the second author was visiting the University of Edinburgh, with support from the Edinburgh Mathematical Society. The second author acknowledges support by an EPSRC Advanced Fellowship EP/D071674/1.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 989-1001
  • MSC (2000): Primary 16Nxx, 16P90
  • DOI: https://doi.org/10.1090/S0894-0347-07-00565-6
  • MathSciNet review: 2328713