P-compact group

From Wikipedia, the free encyclopedia

A p-compact group is a mathematical object, studied in the part of mathematics called algebraic topology. A p-compact group is a homotopical version of a compact Lie group, but with all the structure concentrated at a single prime p.

Examples include the p-completion of a compact connected Lie group, and the "Sullivan spheres", i.e., the p-completion of a sphere of dimension 2n-1, if n divides p-1.

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, just over the p-adic integers instead of the integers.