A uniqueness result for orthogonal groups as 2-compact groups

Abstract

Two connected compact Lie groups are isomorphic if and only if their maximal torus normalizers are isomorphic. It is conjectured that this result generalizes to p-compact groups. Here, we prove the generalization for orthogonal groups O(n), the special orthogonal groups SO(2k + 1) and the spinor groups Spin(2k + 1) considered as 2-compact groups.

Normalizers of tori

“…In contrast, it is not known that the normalizer of a maximal 2-discrete torus in a connected 2-compact group X determines X up to equivalence. However, this seems likely to be true [27,23,2], and we hope that the results of this paper will eventually contribute to a classification of connected 2-compact groups.…”