nLab
G-universe

Contents

Contents

Idea

In equivariant stable homotopy theory over a compact Lie group GG, a GG-universe is a GG-representation that contains “all” representations of GG of sorts.

This is used in one definition of G-spectra via looping and delooping by representation spheres.

Definition

A G-universe in this context is (e.g. Greenlees-May, p. 10) an infinite dimensional real inner product space equipped with a linear GG-action that is the direct sum of countably many copies of a given set of (finite dimensional) representations of GG, at least containing the trivial representation on \mathbb{R} (so that UU contains at least a copy of \mathbb{R}^\infty).

References

Last revised on November 19, 2015 at 14:23:48. See the history of this page for a list of all contributions to it.