# nLab equivariant dgc-algebra

Contents

### Context

#### Representation theory

representation theory

geometric representation theory

## Theorems

#### Algebra

higher algebra

universal algebra

and

# Contents

## Definition

Let $G$ be a finite group.

###### Example

A $G$-equivariant dgc-algebra in the sense of equivariant rational homotopy theory is a functor

$G Orbits \longrightarrow dgcAlgebras$

from the orbit category of $G$ to the category of dgc-algebras.

## Examples

###### Example

(equivariant PL de Rham complex)

Let $S \in G SimplicialSets$ be a simplicial set equipped with $G$-action, for instance the singular simplicial set of a topological G-space.

The equivariant PL de Rham complex of $S$ is the equivariant dgc-algebra given as the functor from the orbit category of $G$ to the category of dgc-algebras

$\array{ G Orbits & \overset{ \Omega^\bullet_{PLdR} \big( Maps(-,X)^G \big) }{\longrightarrow} & dgcAlgebras \\ G/H &\mapsto& \Omega^\bullet_{PLdR} \big( X^H \big) }$

which to a coset space $G/H$ assigns the PL de Rham complex of the $H$-fixed locus $X^H \subset X$.

## References

Last revised on September 29, 2020 at 05:57:52. See the history of this page for a list of all contributions to it.