Alladi Ramakrishnan Hall

Infinitely many non-extendable semigroups

Panchugopal Bikram

Ben Gurion University

We introduce a cocycle conjugacy invariant, the subfactor
index, for $E_0$-semigroups on non type I factors. We prove that the subfactor
index is multiplicative over tensor product of $E_0$-semigroups. We prove that
factor subfactor index of CAR flows will be some number in $(1, 2]$.
Which will provide infinitely many pairwise non cocycle conjugate non
extendable $E_0$-semigroups on type II_1, II infinity and III factors.