Published online by Cambridge University Press: 24 October 2008
Let M be a von Neumann algebra acting on a Hilbert space , and let G be a locally compact group. We consider an extension
of G by
, the unitary group of M. If the triple
satisfies an additional axiom, we say that it is an extended covariant system. We define a Hilbert space
and operators
, acting on
. The von Neumann algebra
is then the covariance algebra of the extended covariant system
, denoted by
.