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
DOI:
https://doi.org/10.1090/S0894-0347-07-00565-6
Published electronically:
April 2, 2007
MathSciNet review:
2328713
Full-text PDF Free Access
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.
- V. A. Ufnarovskij, Combinatorial and asymptotic methods in algebra [ MR1060321 (92h:16024)], Algebra, VI, Encyclopaedia Math. Sci., vol. 57, Springer, Berlin, 1995, pp. 1–196. MR 1360005, DOI https://doi.org/10.1007/978-3-662-06292-0_1
- E. S. Golod and I. R. Šafarevič, On the class field tower, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 261–272 (Russian). MR 0161852
- Günter R. Krause and Thomas H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Revised edition, Graduate Studies in Mathematics, vol. 22, American Mathematical Society, Providence, RI, 2000. MR 1721834 small L W Small, private communication, February 2004.
- L. W. Small, J. T. Stafford, and R. B. Warfield Jr., Affine algebras of Gel′fand-Kirillov dimension one are PI, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 3, 407–414. MR 778674, DOI https://doi.org/10.1017/S0305004100062976
- Agata Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), no. 2, 427–436. MR 1793911, DOI https://doi.org/10.1006/jabr.2000.8451
Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 16Nxx, 16P90
Retrieve articles in all journals with MSC (2000): 16Nxx, 16P90
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
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.
