# Conformal nets and strong additivity

In this talk we will explain that the fixed point net of a strongly
additive net under the action of a compact group is also strongly
additive generalizing previous results. What is actually proved is a
stronger property for the
pair of nets which is called a strongly additive pair. We explain that
a key theorem about the induction of a pair of nets which was proved
previously under finite index conditions can be generalized to strongly
additive pair with simpler proof. This is then used to classify
conformal nets with central charge 1 which satisfy a spectrum condition
but are not necessarily rational.