Abstract
We describe the primitive central idempotents of the group algebra over a number field of finite monomial groups. We give also a description of the Wedderburn decomposition of the group algebra over a number field for finite strongly monomial groups. Further, for this class of group algebras, we describe when the number of simple components agrees with the number of simple components of the rational group algebra. Finally, we give a formula for the rank of the central units of the group ring over the ring of integers of a number field for a strongly monomial group.
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Presented by Radha Kessar.
The research is supported by the grant PN-II-ID-PCE-2012-4-0100 and by the Research Foundation Flanders (FWO - Vlaanderen).
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Olteanu, G., Van Gelder, I. On Idempotents and the Number of Simple Components of Semisimple Group Algebras. Algebr Represent Theor 19, 315–333 (2016). https://doi.org/10.1007/s10468-015-9575-2
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DOI: https://doi.org/10.1007/s10468-015-9575-2