Abstract
We prove that the partition of Markov diffusions into reciprocal classes is equivalent to the partition of the one parameter symmetry groups of second order linear partial differential operators under gauge equivalence. In order to do so we explicit the system of Determining Equations which characterize the symmetries of a second order linear p.d.e. and we prove that the set of compatibility conditions for this system only depends on the reciprocal class. We then show that the reciprocal class of a Markov diffusion is preserved under the symmetries of the associated partial differential operator
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