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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
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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

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