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 $G$ 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.
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