Alladi Ramakrishnan Hall

Many CCR flows

R. Srinivasan

CMI

Using Araki-Woods representations of the canonical commutation
relations(CCR)
algebras, we construct a large family of $E_0$-semigroups on type $III$
factors, which we call as Toeplitz CCR flows. In the simplest case, which
we
call as CCR flows, we classify them up to cocycle conjugacy. This
construction provides uncountably many mutually non-cocycle-conjugate
$E_0$-semigroups on all hyperfinite type ${III}_{\lambda}$ factors. We also
discuss
the extendability of Toeplitz CCR flows. This is mostly a joint work with
Oliver T. Margetts, and a small part of it is a joint work with Masaki
Izumi.