Geodesic
An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
Lenagan, T.1 ; Smoktunowicz, Agata2, 1
1 Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
2 Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956 Warsaw 10, Poland
Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 989-1001

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-07-00565-6

Lenagan, T. 1 ; Smoktunowicz, Agata 2, 1

1 Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
2 Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956 Warsaw 10, Poland 
@article{10_1090_S0894_0347_07_00565_6,
     author = {Lenagan, T. and Smoktunowicz, Agata},
     title = {An infinite dimensional affine nil algebra with finite {Gelfand-Kirillov} dimension},
     journal = {Journal of the American Mathematical Society},
     pages = {989--1001},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2007},
     doi = {10.1090/S0894-0347-07-00565-6},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-07-00565-6/}
}
TY  - JOUR
AU  - Lenagan, T.
AU  - Smoktunowicz, Agata
TI  - An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
JO  - Journal of the American Mathematical Society
PY  - 2007
SP  - 989
EP  - 1001
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-07-00565-6/
DO  - 10.1090/S0894-0347-07-00565-6
ID  - 10_1090_S0894_0347_07_00565_6
ER  - 
%0 Journal Article
%A Lenagan, T.
%A Smoktunowicz, Agata
%T An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
%J Journal of the American Mathematical Society
%D 2007
%P 989-1001
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-07-00565-6/
%R 10.1090/S0894-0347-07-00565-6
%F 10_1090_S0894_0347_07_00565_6
Lenagan, T.; Smoktunowicz, Agata. An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension. Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 989-1001. doi: 10.1090/S0894-0347-07-00565-6

[1] Ufnarovskij, V. A. Combinatorial and asymptotic methods in algebra [ MR1060321 (92h:16024)] 1995 1 196

[2] Golod, E. S., Å Afareviä, I. R. On the class field tower Izv. Akad. Nauk SSSR Ser. Mat. 1964 261 272

[3] Krause, Gã¼Nter R., Lenagan, Thomas H. Growth of algebras and Gelfand-Kirillov dimension 2000

[4] Small, L. W., Stafford, J. T., Warfield, R. B., Jr. Affine algebras of Gel′fand-Kirillov dimension one are PI Math. Proc. Cambridge Philos. Soc. 1985 407 414

[5] Smoktunowicz, Agata Polynomial rings over nil rings need not be nil J. Algebra 2000 427 436

Cité par Sources :