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An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
Author(s):
T.
H.
Lenagan;
Agata
Smoktunowicz
Journal:
J. Amer. Math. Soc.
20
(2007),
989-1001.
MSC (2000):
Primary 16Nxx, 16P90
Posted:
April 2, 2007
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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.
References:
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- 1.
- V A Ufnarovskij, Combinatorial and asymptotic methods in algebra, Algebra, VI, 1-196, Encyclopaedia Math. Sci., 57, Springer, Berlin, 1995. MR 1360005
- 2.
- E S Golod, and I R Shafarevich, On the class field tower, Izv. Akad. Nauk. SSSR Mat. Ser. 28 (1964), 261-272 (in Russian). MR 0161852 (28:5056)
- 3.
- G R Krause and T H Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Revised edition. Graduate Studies in Mathematics, 22. American Mathematical Society, Providence, RI, 2000. MR 1721834 (2000j:16035)
- 4.
- L W Small, private communication, February 2004.
- 5.
- L W Small, J T Stafford and R B Warfield, Jr, Affine algebras of Gelfand-Kirillov dimension one are PI, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 3, 407-414. MR 778674 (86g:16025)
- 6.
- Agata Smoktunowicz, Polynomial rings over nil rings need not be nil, Journal of Algebra 233 (2000), 427-436. MR 1793911 (2001i:16045)
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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:
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
Posted:
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 of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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