Some algebraic properties of differential operators
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 pseudodiff...
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| Format: | Article |
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AIP Publishing
2018
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| Online Access: | http://hdl.handle.net/1721.1/115839 https://orcid.org/0000-0001-6809-4128 https://orcid.org/0000-0002-2860-7811 |
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| author | Carpentier, Sylvain De Sole, Alberto Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Carpentier, Sylvain De Sole, Alberto Kac, Victor |
| author_sort | Carpentier, Sylvain |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:27:57Z |
| format | Article |
| id | mit-1721.1/115839 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:27:57Z |
| publishDate | 2018 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1158392022-09-30T14:36:33Z Some algebraic properties of differential operators Carpentier, Sylvain De Sole, Alberto Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Carpentier, Sylvain De Sole, Alberto Kac, Victor 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. 2018-05-24T14:30:15Z 2018-05-24T14:30:15Z 2012-06 2012-01 2018-05-24T12:03:23Z Article http://purl.org/eprint/type/JournalArticle 0022-2488 1089-7658 http://hdl.handle.net/1721.1/115839 Carpentier, Sylvain et al. “Some Algebraic Properties of Differential Operators.” Journal of Mathematical Physics 53, 6 (June 2012): 063501 © 2012 American Institute of Physics https://orcid.org/0000-0001-6809-4128 https://orcid.org/0000-0002-2860-7811 http://dx.doi.org/10.1063/1.4720419 Journal of Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf AIP Publishing arXiv |
| spellingShingle | Carpentier, Sylvain De Sole, Alberto Kac, Victor Some algebraic properties of differential operators |
| title | Some algebraic properties of differential operators |
| title_full | Some algebraic properties of differential operators |
| title_fullStr | Some algebraic properties of differential operators |
| title_full_unstemmed | Some algebraic properties of differential operators |
| title_short | Some algebraic properties of differential operators |
| title_sort | some algebraic properties of differential operators |
| url | http://hdl.handle.net/1721.1/115839 https://orcid.org/0000-0001-6809-4128 https://orcid.org/0000-0002-2860-7811 |
| work_keys_str_mv | AT carpentiersylvain somealgebraicpropertiesofdifferentialoperators AT desolealberto somealgebraicpropertiesofdifferentialoperators AT kacvictor somealgebraicpropertiesofdifferentialoperators |