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GK–DIMENSION OF ALGEBRAS WITH MANY GENERIC RELATIONS*

Published online by Cambridge University Press:  01 May 2009

AGATA SMOKTUNOWICZ
AGATA SMOKTUNOWICZ*
Affiliation:
Maxwell Institute of Mathematical Sciences, School of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland e-mail: A.Smoktunowicz@ed.ac.uk
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Abstract

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We prove some results on algebras, satisfying many generic relations. As an application we show that there are Golod–Shafarevich algebras which cannot be homomorphically mapped onto infinite dimensional algebras with finite Gelfand–Kirillov dimension. This answers a question of Zelmanov (Some open problems in the theory of infinite dimensional algebras, J. Korean Math. Soc. 44(5) 2007, 1185–1195).

Keywords

16DXX16N60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 253 - 256
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Golod, E. S., On nil algebras and finitely approximable P-groups, Izv. Akad. Nauk SSSR Ser. Math. 28 (1964), 273–276.Google Scholar
2.Golod, E. S. and Shafarevich, I. R., On the class field tower, Izv. Akad. Nauk SSSR Ser. Math. 28 (1964), 261–272.Google Scholar
3.Krause, G. and Lenagan, T. H., Growth of algebras and Gelfand–Kirillov dimension, revised edition (American Mathematical Society, Providence, RI, USA, 2000).Google Scholar
4.Zelmanov, E., Some open problems in the theory of infinite dimensional algebras, J. Korean Math. Soc. 44 (5) 2007, 1185–1195.CrossRefGoogle Scholar