  von Neumann algebras have been playing an increasingly important role in the
context of gauge theories and gravity. The crossed product presents a natural
method for implementing constraints through the commutation theorem, rendering
it a useful tool for constructing gauge invariant algebras. The crossed product
of a Type III algebra with its modular automorphism group is semifinite, which
means that the crossed product regulates divergences in local quantum field
theories. In this letter, we find a sufficient condition for the semifiniteness
of the crossed product of a type III algebra with any locally compact group
containing the modular automorphism group. Our condition surprisingly implies
the centrality of the modular flow in the symmetry group, and we provide
evidence for the necessity of this condition. Under these conditions, we
construct an associated trace which computes physical expectation values. We
comment on the importance of this result and and its implications for subregion
physics in gauge theory and gravity.
