Double Numbers and Two Dimensional Anomaly Free Field Models
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In ref. it has been made the certain assertions concerning possibility of nonanomalous quantization of the string inspired model  of two dimensional gravity. In some variables this model can be described by the first class constraints as in the case of ordinary relativistic bosonic string in two dimensional space-time.The ring of double numbers is natural tool for woking with the two dimensional Minkowski space.We propose the model of the two-dimensional quantum gravity wich is invariant with respect to the two-dimensional superluminal Lorentz transformation.The Virasoro algebra of the quantum gravity model defined over double number ring is found to be without conformal anomaly.