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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…
Differential Conformal Superalgebras and their Forms
Victor Kac, Michael Lau, Arturo Pianzola
We introduce the formalism of differential conformal superalgebras, which we show leads to the "correct" automorphism group functor and accompanying descent theory in the conformal…