We present a quasi-Lie bialgebra (QLBA) quantization problem which comes from
an algebraic reformulation of the Nambu-Goto string theory and invariant
charges by Pohlmeyer and Rehren. This QLBA structure depends on a symmetric
bivector (coming from a Minkowski metric) and is built on the free Lie algebra
on a finite dimensional vector space. We solve this problem when the bivector
has rank 1 or 2.