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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension


Authors: T. H. Lenagan and Agata Smoktunowicz
Journal: J. Amer. Math. Soc. 20 (2007), 989-1001
MSC (2000): Primary 16Nxx, 16P90
Published electronically: April 2, 2007
MathSciNet review: 2328713
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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
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
Email: agatasm@impan.gov.pl

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00565-6
PII: S 0894-0347(07)00565-6
Keywords: Nil algebra, growth of algebras, Gelfand-Kirillov dimension.
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.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.