G-universe

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

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

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

- John Greenlees, Peter May,
*Equivariant stable homotopy theory*(pdf)

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