A remark on the holonomy group of a normal state over a hyperfinite von Neumann algebra

We will show that in a hyperfinite von Neumann algebra M acting on a separable Hilbert space, there exists a constant N ϵ N such that for an arbitrary ϑ ϵ [0, 2π] there are invertible a1,…,aN ϵ M+ with aN…a1 = eiϑ1. As a consequence, it can be shown that U(1) is isomorphically contained in the holonomy group at every normal state over M.