nLab
spectrum with G-action
Contents
Context
Stable Homotopy theory
Representation theory
representation theory

geometric representation theory

Ingredients
Definitions
representation , 2-representation , ∞-representation

group , ∞-group

group algebra , algebraic group , Lie algebra

vector space , n-vector space

affine space , symplectic vector space

action , ∞-action

module , equivariant object

bimodule , Morita equivalence

induced representation , Frobenius reciprocity

Hilbert space , Banach space , Fourier transform , functional analysis

orbit , coadjoint orbit , Killing form

unitary representation

geometric quantization , coherent state

socle , quiver

module algebra , comodule algebra , Hopf action , measuring

Geometric representation theory
D-module , perverse sheaf ,

Grothendieck group , lambda-ring , symmetric function , formal group

principal bundle , torsor , vector bundle , Atiyah Lie algebroid

geometric function theory , groupoidification

Eilenberg-Moore category , algebra over an operad , actegory , crossed module

reconstruction theorems

Theorems
Contents
Idea
For $G$ a topological group , a spectrum with $G$ -action is a spectrum equipped with an action of $G$ . In other words, it is a functor from $BG$ to the (infinity,1)-category of spectra. The stable homotopy theory of spectra with $G$ -action is part of the subject of equivariant stable homotopy theory .

Spectra with $G$ -action are sometimes called “doubly naive” $G$ -spectra. They are even more naive than naive G-spectra , and can be identified with the full subcategory of G-spectra consisting of “Borel-complete” $G$ -spectra (see Prop. 6.17 in MNN or Thm. II.2.7 in NS ).

See also
References
Last revised on December 19, 2017 at 12:40:03.
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