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# Contents

## Definition

Let $q$ be a prime power, $V$ a vector space of dimension $n$ over the finite field $\mathbf{F}_q$, and $\mathbf {G L}(V)$, the general linear group of invertible linear transformations on $V$.

The ring of Dickson invariants is defined as the $GL(V)$-invariants $Sym(V)^{\mathbf{G L}(V)}$ in the symmetric algebra on $V$.

This is a graded polynomial algebra on $n$ variables. The degrees of the generators are $q^n - q^i$ for $i=0,\dots,n-1$.

See Wilkerson 83.

## Properties

### Spaces with DI cohomology

The infinity-groups whose classifying spaces/deloopings have mod 2 ordinary cohomology given by rank $n$ Dickson invariants are precisely these 4 of which the first three are compact Lie groups and the last one in a 2-compact group:

$n=$1234
$DI(n)=$Z/2SO(3)G2G3

## References

Named after Leonard Dickson.

Last revised on August 26, 2019 at 12:16:05. See the history of this page for a list of all contributions to it.