  In a 1+1 dimensional model of plane gravitational waves the flux-holonomy
algebra of loop quantum gravity is modified in such a way that the new basic
operators satisfy canonical commutation relations. Thanks to this construction
it is possible to find kinematical solutions for unidirectional plane
gravitational waves with finite geometric expectation values and fluctuations,
which was problematic in a more conventional approach in a foregoing paper by
the author and coauthors.
