University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > The Loewy structures of the principal indecomposable modules (PIM's) for small alternating groups in characteristic 2 and 3

The Loewy structures of the principal indecomposable modules (PIM's) for small alternating groups in characteristic 2 and 3

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  • UserHa Thu Nguyen
  • ClockFriday 17 January 2014, 15:30-16:30
  • HouseCMS, MR5.

If you have a question about this talk, please contact Julian Brough.

Let G be a finite group, k be an algebraically closed field. It is well-known that when char k does not divide |G|, every finite dimensional kG-module is semisimple. However, this is not the case if char k divides |G|. Nevertheless, in this case, we can visualize any finite dimensional kG-module as made up of many semisimple layers via its Loewy/socle series. In this talk, we will give a quick review on various ways of describing the structure of the PIM ’s of a finite group algebra, including their module diagrams, and the deep and beautiful results on the structures of the PIM ’s in blocks with cyclic defects. We will then work out the explicit Loewy structures of the principal indecomposable modules (PIM’s) for A_6, A_7, A_8, and A_9 in characteristic 3, and if time permits, in characteristic 2.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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