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Trace methods in twisted group algebras, II

Authors: J. M. Osterburg and D. S. Passman
Journal: Proc. Amer. Math. Soc. 130 (2002), 3495-3506
MSC (2000): Primary 16S35
Published electronically: March 29, 2002
MathSciNet review: 1918825
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Abstract: In this note, we continue our discussion of trace methods in twisted group algebras. Specifically, we obtain the twisted analog of Bass' theorem on the traces of idempotents in ordinary group algebras. Indeed, we show that with suitable normalization, the characteristic $0$ trace values of an idempotent are all contained in a cyclotomic field. The proof is a variant of the original argument combined with a reduction to finitely presented groups.

References [Enhancements On Off] (What's this?)

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  • 2. G. J. Janusz, Algebraic Number Fields, $2^{\text{nd}}$ edition, American Math. Soc., Providence, 1996. MR 96j:11137
  • 3. D. S. Passman, The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. MR 81d:16001; reprint MR 86j:16001
  • 4. D. S. Passman, Trace methods in twisted group algebras, Proc. AMS 129 (2001), 943-946. MR 2001g:16054
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Additional Information

J. M. Osterburg
Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221

D. S. Passman
Affiliation: Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706

Received by editor(s): July 13, 2001
Published electronically: March 29, 2002
Additional Notes: The first author’s research was supported by the Taft Committee of the University of Cincinnati. He would also like to thank the Mathematics Department of the University of Wisconsin for its hospitality. The second author’s research was supported in part by NSF Grant DMS-9820271.
Communicated by: Lance W. Small
Article copyright: © Copyright 2002 American Mathematical Society

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