  We identify the maximal chiral algebra of conformal cyclic orbifolds. In
terms of this extended algebra, the orbifold is a rational and diagonal
conformal field theory, provided the mother theory itself is also rational and
diagonal. The operator content and operator product expansion of the cyclic
orbifolds are revisited in terms of this algebra. The fusion rules and fusion
numbers are computed via the Verlinde formula. This allows one to predict which
conformal blocks appear in a given four-point function of twisted or untwisted
operators, which is relevant for the computation of various entanglement
measures in one-dimensional critical systems.
