nLab
linear representation

Contents

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

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

Characters of linear representations

See characters of linear representations.

Characteristic classes of linear representations

Under the Atiyah-Segal completion map linear representations of a group GG induce topological K-theory classes on the classifying space BGB 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 09:18:03. See the history of this page for a list of all contributions to it.