Proceedings of the American Mathematical Society

Author(s): J. M. Osterburg; D. S. Passman
Journal: Proc. Amer. Math. Soc. 130 (2002), 3495-3506.
MSC (2000): Primary 16S35
Posted: March 29, 2002
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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

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.

1.: H. Bass, Euler characteristics and characters of discrete groups, Invent. Math. 35 (1976), 155-196. MR 55:5764
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
5.: S. K. Sehgal, Topics in Group Rings, Marcel Dekker, New York, 1978. MR 80j:16001

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16S35

J. M. Osterburg
Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221
Email: james.osterburg@math.uc.edu

D. S. Passman
Affiliation: Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

DOI: 10.1090/S0002-9939-02-06483-3
PII: S 0002-9939(02)06483-3
Received by editor(s): July 13, 2001
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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