Trace methods in twisted group algebras, II
HTML articles powered by AMS MathViewer
- by J. M. Osterburg and D. S. Passman PDF
- Proc. Amer. Math. Soc. 130 (2002), 3495-3506 Request permission
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
- Hyman Bass, Euler characteristics and characters of discrete groups, Invent. Math. 35 (1976), 155–196. MR 432781, DOI 10.1007/BF01390137
- Gerald J. Janusz, Algebraic number fields, 2nd ed., Graduate Studies in Mathematics, vol. 7, American Mathematical Society, Providence, RI, 1996. MR 1362545, DOI 10.1090/gsm/007
- I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. MR 81
- D. S. Passman, Trace methods in twisted group algebras, Proc. Amer. Math. Soc. 129 (2001), no. 4, 943–946. MR 1707017, DOI 10.1090/S0002-9939-00-05613-6
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
Additional Information
- 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
- MR Author ID: 136635
- Email: passman@math.wisc.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3495-3506
- MSC (2000): Primary 16S35
- DOI: https://doi.org/10.1090/S0002-9939-02-06483-3
- MathSciNet review: 1918825