Centralizers (left, right, and
double) of rings and algebras have received much attention recently, and seem likely
to become an important topic in ring theory. They have proved quite useful
in Banach algebra theory, and a good deal of work has been done on the
computation of centralizers for various Banach algebras. In this paper we
compute the left centralizers of a twisted group algebra, a generalization of
the group algebra of locally compact group, which includes as special cases
the covariance algebras of quantum field theory, and the group algebras
of separable group extensions (explicitly given in terms of the subgroup
algebra and quotient group). We give a representation of the algebra of left
centralizers of a “locally continuous” twisted group algebra as an algebra of
vector-valued measures with “twisted convolution”. This result gives more than
explicit computation of centralizers. The form of the result enables us to
investigate isometric isomorphisms between twisted group algebras along lines
previously pursued for ordinary group algebras. In some cases we get a complete
description of possible isomorphism classes in terms of orbits in a cohomology
set.
