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 | References | Similar Articles | Additional Information

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

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.