Can one factor the classical adjoint of a generic matrix?
| dc.creator | Bergman, George M. | |
| dc.date | 2003-06-08 | |
| dc.date | 2004-08-08 | |
| dc.date.accessioned | 2026-07-07T08:06:08Z | |
| dc.date.available | 2026-07-07T08:06:08Z | |
| dc.description | Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its classical adjoint. It is shown that if char k=0 and n is odd, then adj(X) is not the product of two noninvertible nxn matrices over k[x_{ij}]. If n is even and >2, a restricted class of nontrivial factorizations occur. The nonzero-characteristic case remains open. The operation adj on matrices arises from the (n-1)st exterior power functor on modules; the same question can be posed for matrix operations arising from other functors. | |
| dc.description | Revised version contains answer to "even n" question left open in original version. (Answer due to Buchweitz & Leuschke; simple proof in this note.) Copy at http://math.berkeley.edu/~gbergman/papers will always have latest version; revisions sent to arXiv only for major changes | |
| dc.identifier | https://arxiv.org/abs/math/0306126 | |
| dc.identifier | http://arxiv.org/abs/math/0306126 | |
| dc.identifier | Transformation Groups, 11 (2006) 7-15 | |
| dc.identifier | doi:10.1007/s00031-005-1101-x | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130506 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 15A23 (primary), 14F05, 55R25 (secondary) | |
| dc.title | Can one factor the classical adjoint of a generic matrix? | |
| dc.type | text |