Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-27T04:05:40.347Z Has data issue: false hasContentIssue false
  • English
  • Français

On the transcendence degree of group algebras of nilpotent groups

Published online by Cambridge University Press:  18 May 2009

Martin Lorenz
Martin Lorenz
Affiliation:
Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26 5300 Bonn 3, West Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a finitely generated (f.g.) torsion-free nilpotent group. Then the group algebra k[G] of G over a field k is a Noetherian domain and hence has a classical division ring of fractions, denoted by k(G). Recently, the division algebras k(G) and, somewhat more generally, division algebras generated by f.g. nilpotent groups have been studied in [3] and [5]. These papers are concerned with the question to what extent the division algebra determines the group under consideration. Here we continue the study of the division algebras k(G) and investigate their Gelfand–Kirillov (GK–) transcendence degree.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 167 - 174
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Bass, H., The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3) 25 (1972), 603–614.CrossRefGoogle Scholar
2.Borho, W. and Kraft, H., Uber die Gelfand-Kirillov-Dimension, Math. Ann. 220 (1976), 1–24.CrossRefGoogle Scholar
3.Farkas, D. R., Schofield, A. H., Snider, R. L. and Stafford, J. T., The isomorphism question for division rings of group rings, Proc. Amer. Math. Soc. 85 (1982), 327–330.Google Scholar
4.Lorenz, M., Primitive ideals in crossed products and rings with finite group actions, Math. Z. 158 (1978) 285–294.CrossRefGoogle Scholar
5.Lorenz, M., Division algebras generated by finitely generated nilpotent groups, J. Algebra 85 (1983), 368–381.CrossRefGoogle Scholar
6.Makar-Limanov, L., The skew field Di contains free subalgebras, Comm. Algebra 11 (1983), 2003–2006.CrossRefGoogle Scholar
7., The algebraic structure of group rings (Wiley-Interscience, 1977).Google Scholar