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

The operator algebra of cyclic orbifolds