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arXiv · 1201.1992

Some algebraic properties of differential operators

Sylvain Carpentier·Alberto De Sole·Victor G. Kac
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Abstract

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that the Dieudonne' determinant of a matrix pseudodifferential operator with coefficients in a differential subring A of K lies in the integral closure of A in K, and we give an example of a 2x2 matrix differential operator with coefficients in A whose Dieudonne' determiant does not lie in A.

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Sylvain Carpentier, Alberto De Sole, Victor G. Kac. 2012-01-10. Some algebraic properties of differential operators. https://doi.org/10.1063/1.4720419

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