Contents

# Contents

## Idea

A linear representation is a representation on a category of vector spaces or similar (Vect, Mod, etc.)

This is the most common flavor of representations. One sometimes considers representations on objects other than linear spaces (such as permutation representations) but often these are called not representations but actions.

## Properties

### Characteristic classes of linear representations

Under the Atiyah-Segal completion map linear representations of a group $G$ induce topological K-theory classes on the classifying space $B G$. Their Chern classes are hence invariants of the linear representations themselves.

See at characteristic class of a linear representation for more.

## References

For more see the references at representation theory.

Last revised on February 1, 2019 at 14:18:03. See the history of this page for a list of all contributions to it.