Some algebraic properties of differential operators
Author(s)Carpentier, Sylvain; De Sole, Alberto; Kac, Victor
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First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield K((∂⁻¹)) of pseudodifferential operators over K by the subalgebra K[∂] of all differential operators. Second, we show that the Dieudonnè 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 then we give an example of a 2 × 2 matrix with entries in A[∂] whose Dieudonnè determinant does not lie in A.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Mathematical Physics
Carpentier, Sylvain et al. “Some Algebraic Properties of Differential Operators.” Journal of Mathematical Physics 53, 6 (June 2012): 063501 © 2012 American Institute of Physics