Trace methods in twisted group algebras
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Abstract:
In this brief note, we discuss trace methods in twisted group algebras. Specifically, we obtain information on the trace of idempotent and nilpotent elements. As is to be expected, if the ground field has positive characteristic, then the arguments used for ordinary group rings carry over to this context with little difficulty. On the other hand, lifting these results to characteristic zero algebras is not straightforward and requires a reduction to finitely presented groups.References
- Irving Kaplansky, Fields and rings, University of Chicago Press, Chicago, Ill.-London, 1969. MR 0269449
- D. S. Passman, Radicals of twisted group rings, Proc. London Math. Soc. (3) 20 (1970), 409–437. MR 271246, DOI 10.1112/plms/s3-20.3.409
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
- A. E. Zalesskiĭ, A certain conjecture of Kaplansky, Dokl. Akad. Nauk SSSR 203 (1972), 749–751 (Russian). MR 0297895
Additional Information
- D. S. Passman
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 136635
- Email: passman@math.wisc.edu
- Received by editor(s): June 14, 1999
- Published electronically: October 16, 2000
- Additional Notes: This research was supported by NSF Grant DMS-9820271. The author would like to thank Prof. Jairo Z. Gonçalves for interesting conversations on this subject.
- Communicated by: Lance W. Small
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 943-946
- MSC (2000): Primary 16S35
- DOI: https://doi.org/10.1090/S0002-9939-00-05613-6
- MathSciNet review: 1707017