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Trace methods in twisted group algebras
Author(s):
D.
S.
Passman
Journal:
Proc. Amer. Math. Soc.
129
(2001),
943-946.
MSC (2000):
Primary 16S35
Posted:
October 16, 2000
MathSciNet review:
1707017
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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:
-
- [K]
- I. Kaplansky, Fields and Rings, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, 1969. MR 42:4345
- [P1]
- D. S. Passman, Radicals of twisted group rings, Proc. London Math. Soc. (3) 20 (1970), 409-437. MR 42:6129
- [P2]
- -, The Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. MR 81d:16001
- [Z]
- A. E. Zalesskii, On a problem of Kaplansky, Soviet Math. 13 (1972), 449-452. MR 45:6947
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Additional Information:
D.
S.
Passman
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
passman@math.wisc.edu
DOI:
10.1090/S0002-9939-00-05613-6
PII:
S 0002-9939(00)05613-6
Received by editor(s):
June 14, 1999
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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