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Properties and examples of FCR-algebras |
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| Authors: | Hanspeter Kraft Lance W. Small Nolan R. Wallach |
| Affiliation: | Mathematisches Institut, Universit?t Basel, Rheinsprung 21, 4051 Basel, Switzerland. e-mail: kraft@math.unibas.ch, CH Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA.?e-mail: lwsmall@ucsd.edu, nwallach@ucsd.edu, US |
| Abstract: | An algebra A over a field k is FCR if every finite dimensional representation of A is completely reducible and the intersection of the kernels of these representations is zero. We give a useful characterization of FCR-algebras and apply this to C *-algebras and to localizations. Moreover, we show that “small” products and sums of FCR-algebras are again FCR. Received: 25 October 2000 |
| Keywords: | Mathematics Subject Classification (2000): 16S10 16D60 16G99 |
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