Let be a prime power, a vector space of dimension over the finite field , and , the general linear group of invertible linear transformations on .
The ring of Dickson invariants is defined as the -invariants in the symmetric algebra on .
This is a graded polynomial algebra on variables. The degrees of the generators are for .
See Wilkerson 83.
The infinity-groups whose classifying spaces/deloopings have mod 2 ordinary cohomology given by rank Dickson invariants are precisely these 4 of which the first three are compact Lie groups and the last one in a 2-compact group:
1 | 2 | 3 | 4 | |
---|---|---|---|---|
Z/2 | SO(3) | G2 | G3 |
(Dwyer-Wilkerson 93, top of p. 38 (2 of 28))
Named after Leonard Dickson.
Clarence Wilkerson, A primer on Dickson invariants, in Haynes Miller, Stewart Priddy (eds.) Proceedings of the Northwestern Homotopy Theory Conference, 1983 (doi:10.1090/conm/019) (pdf)
William Dwyer, Clarence Wilkerson, A new finite loop space at the prime two, J. Amer. Math. Soc. 6 (1993), 37-64 (doi:10.1090/S0894-0347-1993-1161306-9)
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