A Proof of the Conjecture by Carpentier-De Sole-Kac
Keaton Stubis
TL;DR
This paper proves a conjecture regarding the Dieudonne' determinant of matrices of differential operators, establishing that under certain conditions, it resides within a specified differential subring.
Contribution
It provides a rigorous proof confirming that matrices with degeneracy degree 1 have their Dieudonne' determinant in the differential subring, advancing understanding in differential algebra.
Findings
Confirmed the conjecture for matrices with degeneracy degree 1
Established the Dieudonne' determinant's location within the differential subring
Enhanced theoretical understanding of differential operators and determinants
Abstract
We prove the following conjecture by S. Carpentier, A. De Sole, and V. G. Kac: Let K be a differential field and R be a differential subring of K. Let M be a matrix whose elements are differential operators with coefficents in R. Then, if M has degeneracy degree 1, the Dieudonne' determinant of M lies in R.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.