Logarithmic Operators in Conformal Field Theory and The ∞-algebra

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It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of ∞-algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary sl(2,C). This method allows us to write differential equations which can be used to find general expression for three and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.