  We present a mathematical construction of new quantum information measures
that generalize the notion of logarithmic negativity. Our approach is based on
formal group theory. We shall prove that this family of generalized negativity
functions, due their algebraic properties, is suitable for studying
entanglement in many-body systems.
  Under mild hypotheses, the new measures are computable entanglement
monotones. Also, they are composable: their evaluation over tensor products can
be entirely computed in terms of the evaluations over each factor, by means of
a specific group law.
  In principle, they might be useful to study separability and (in a future
perspective) criticality of mixed states, complementing the role of R\'enyi's
entanglement entropy in the discrimination of conformal sectors for pure
states.
