“…Some subalgebras of these orbifold algebras appear earlier in Refs. [13,12,14], and the role of these subalgebras in cyclic orbifolds was emphasized by Fuchs, Klemm and Schmidt [12]. With the help of the orbifold algebras, we find that all the familiar constructions of conformal field theory have their counterparts in the orbifolds, including affine-Sugawara constructions [15,16,17,18], coset constructions [15,16,19,20] and affine-Virasoro constructions [21,22,23], as well as SL(2,R)-Ward identities [24] and null-state differential equations of BPZ type.…”