Geometric and Topological Aspects of the Representation Theory of Finite Groups by Jon F. Carlson & Srikanth B. Iyengar & Julia Pevtsova

Author:Jon F. Carlson & Srikanth B. Iyengar & Julia Pevtsova
Language: eng
Format: epub
ISBN: 9783319940335
Publisher: Springer International Publishing

Lemma 3.2

Let such that . Then, there is such that for all P.

Proof

Let D be a hyperfocal subalgebra of the source algebra A of B. That is, D is a P-stable subalgebra of A such that and , where u runs over a set of representatives of in P. For D and P, define . Since , this is well defined, and extends linearly to A. A trivial verification shows that this is an -algebra automorphism of A which acts as the identity on D. The image of the p-power root of unity in k is 1, and hence .

Lemma 3.3

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