Members’ Seminar

We present an overview of elementary methods to study extensions of modular representations of various types of "groups". We shall begin by discussing actions of an elementary abelian $p$-group, $E = (Z/p)^r$, on finite dimensional vector spaces over a field $k$ of characteristic $p > 0$. This leads us to the broader study of the representations of a restricted Lie algebra $g$ on $k$-vector spaces. We briefly mention how the questions raised and the techniques developed can be extended to modular representations of an arbitrary finite group scheme over $k$. We then look more closely at the context of modular representations of an arbitrary finite group.