  The interaction of various algebraic structures describing fusion, braiding
and group symmetries in quantum projective field theory is an object of an
investigation in the paper. Structures of projective Zamolodchikov al- gebras,
their represntations, spherical correlation functions, correlation characters
and envelopping QPFT-operator algebras, projective \"W-algebras, shift
algebras, braiding admissible QPFT-operator algebras and projective
G-hypermultiplets are explored. It is proved (in the formalism of shift
algebras) that sl(2,C)-primary fields are characterized by their projective
weights and by the hidden additive weight, a hidden quantum number discovered
in the paper (some discussions on this fact and its possible relation to a
hidden 4-dimensional QFT maybe found in the note by S.Bychkov, S.Plotnikov and
D.Juriev, Uspekhi Matem. Nauk 47(3) (1992)[in Russian]). The special attention
is paid to various constructions of projective G-hyper- multiplets
(QPFT-operator algebras with G-symmetries).
