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|a Carpentier, Sylvain
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Kac, Victor
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|a De Sole, Alberto
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|a Kac, Victor
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|a Rational matrix pseudodifferential operators
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|b Springer-Verlag,
|c 2015-01-15T19:26:35Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/92902
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|a The skewfield K(∂) of rational pseudodifferential operators over a differential field K is the skewfield of fractions of the algebra of differential operators K[∂]. In our previous paper, we showed that any H ∈ K(∂) has a minimal fractional decomposition H = AB[superscript −1] , where A,B ∈ K[∂], B ≠ 0, and any common right divisor of A and B is a non-zero element of K . Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-zero element of K[∂] . In the present paper, we study the ring M[subscript n](K(∂)) of n × n matrices over the skewfield K(∂). We show that similarly, any H ∈ M[subscript n](K(∂)) has a minimal fractional decomposition H = AB[superscript −1], where A,B ∈ M[subscript n](K[∂]), B is non-degenerate, and any common right divisor of A and B is an invertible element of the ring M[subscript n](K[∂]). Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-degenerate element of M[subscript n](K[∂]). We give several equivalent definitions of the minimal fractional decomposition. These results are applied to the study of maximal isotropicity property, used in the theory of Dirac structures.
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|a National Science Foundation (U.S.)
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|a en_US
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|a Article
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|t Selecta Mathematica
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