University of Birmingham > Talks@bham > Algebra seminar  > Endotrivial modules, local group theory, and homotopy theory

Endotrivial modules, local group theory, and homotopy theory

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For G a finite group and k a field of characteristic p, an endotrivial module is a kG-module M such that End(M) is isomorphic to a trivial module plus a projective module. Equivalence classes of such modules form an abelian group under tensor product. It has has long been a quest to calculate this abelian group, for any finite group G, starting with work of Dade in the 70s. In my talk I’ll explain how this question via homotopy theory reduces to the calculation of a certain finite p’-group, describable in terms of the p-local structure of G. The talk will then explain a number of examples where this can be calculated, such as for the Monster.

This talk is part of the Algebra seminar series.

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