In mathematics, in particular algebraic topology, a p-compact group is (roughly speaking) a space that is a homotopical version of a compact Lie group, but with all the structure concentrated at a single prime p. This concept was introduced by Dwyer and Wilkerson. Subsequently the name homotopy Lie group has also been used.
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Examples
Examples include the p-completion of a compact and connected Lie group, and the Sullivan spheres, i.e. the p-completion of a sphere of dimension
2n − 1,if n divides p − 1.
Classification
The classification of p-compact groups states that there is a 1-1 correspondence between connected p-compact groups, and root data over the p-adic integers. This is analogous to the classical classification of connected compact Lie groups, with the p-adic integers replacing the rational integers.