  In these proceedings, we discuss non-commutativity in closed string theory.
In analogy to the open-string sector, for closed strings we first motivate a
cyclic double commutator to be evaluated for backgrounds with geometric or
non-geometric fluxes. A non-trivial result for such an expression indicates a
non-associative structure. Second, we define a conformal field theory at linear
order in background fluxes and compute correlation functions therein. From
these we motivate a tri-product which captures non-commutative and
non-associative effects.
