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Title: Projective splittings of modules of differential operators on the line

Abstract: As modules of the Lie algebra of vector fields on the line, the differential operators between modules of tensor densities are generically split under the projective subalgebra (the infinitesimal linear fractional transformations). This splitting has been the topic of several studies over the past decade; in particular, Cohen, Manin, and Zagier determined the formula for composition in terms of it. We will discuss these results and certain generalizations to the singular (not projectively split) cases.

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