Baire Category And Laurent Extensions
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 824-830
Voir la notice de l'article provenant de la source Cambridge University Press
Based on a strategy of Kaplansky ([3]), Dixmier proved that a prime, separable C*-algebra is primitive ([1]). As a consequence, when the C*-closure of a countable discrete group is prime, it is primitive. The argument may be regarded as a clever application of the Baire Category Theorem to the spectrum of irreducible representations.The present note is the first step in adapting this technique to abstract group algebras. For which groups G is the primitive ideal space of k[G] a Baire space? One corollary of our main result is that the space is Baire when k is an uncountable field and G is a polycyclic-by-finite group. This gives an alternate proof of a special case of Passman's theorem that such a k[G] will be primitive when its center is k ([4], p. 379).
Farkas, Daniel R. Baire Category And Laurent Extensions. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 824-830. doi: 10.4153/CJM-1979-077-4
@article{10_4153_CJM_1979_077_4,
author = {Farkas, Daniel R.},
title = {Baire {Category} {And} {Laurent} {Extensions}},
journal = {Canadian journal of mathematics},
pages = {824--830},
year = {1979},
volume = {31},
number = {4},
doi = {10.4153/CJM-1979-077-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-077-4/}
}
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[4] 4. Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, N.Y., 1977). Google Scholar
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