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The semicentre of a group algebra

Published online by Cambridge University Press:  20 January 2009

Paul Wauters
Paul Wauters
Affiliation:
Department of Mathematics, Limburgs Universitair Centrum, Diepenbeek, Belgium, E-mail address: [email protected]
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We study the semicentre of a group algebra K[G] where K is a field of characteristic zero and G is a polycyclic-by-finite group suchthat Δ(G) is torsion-free abelian. Several properties about the structure of this ring are proved, in particular as to when is the semicentre a UFD. Examples are constructed when this is not the case. We also prove necessary and sufficient conditions for every normal element of K[G] which belongs to K[Δ(G)] to be the product of a unit and a semi-invariant.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 95 - 111
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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