Factoring the Adjoint and Maximal Cohen--Macaulay Modules over the Generic Determinant

Simple item page
dc.creatorBuchweitz, Ragnar-Olaf
dc.creatorLeuschke, Graham J.
dc.date2005-05-15
dc.date2006-04-17
dc.date.accessioned2026-07-07T06:39:57Z
dc.date.available2026-07-07T06:39:57Z
dc.descriptionA question of Bergman asks whether the adjoint of the generic square matrix over a field can be factored nontrivially as a product of square matrices. We show that such factorizations indeed exist over any coefficient ring when the matrix has even size. Establishing a correspondence between such factorizations and extensions of maximal Cohen--Macaulay modules over the generic determinant, we exhibit all factorizations where one of the factors has determinant equal to the generic determinant. The classification shows not only that the Cohen--Macaulay representation theory of the generic determinant is wild in the tame-wild dichotomy, but that it is quite wild: even in rank two, the isomorphism classes cannot be parametrized by a finite-dimensional variety over the coefficients. We further relate the factorization problem to the multiplicative structure of the $\Ext$--algebra of the two nontrivial rank-one maximal Cohen--Macaulay modules and determine it completely.
dc.description44 pages, final version of the work announced in math.RA/0408425, to appear in the American Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0505315
dc.identifierhttp://arxiv.org/abs/math/0505315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101272
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.subject13C14, 14C40
dc.titleFactoring the Adjoint and Maximal Cohen--Macaulay Modules over the Generic Determinant
dc.typetext

Files

Collections

arXiv