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Singular degree of a rational matrix pseudodifferential operator
Sylvain Carpentier, Alberto De Sole, Victor G. kac
In our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is…
Some remarks on non-commutative principal ideal rings
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are…
Rational matrix pseudodifferential operators
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
The skewfield K(d) of rational pseudodifferential operators over a differential field K is the skewfield of fractions of the algebra of differential operators K[d]. In our previous…
Some algebraic properties of differential operators
Sylvain Carpentier, Alberto De Sole, Victor G. Kac
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 subal…
Calculus structure on the Lie conformal algebra complex and the variational complex
Alberto De Sole, Pedram Hekmati, Victor Kac
We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [DSK]. A…