Document Type

Article

Date

4-17-2006

Embargo Period

11-15-2011

Disciplines

Mathematics

Description/Abstract

A 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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0505315

Source

Harvested from arXiv.org

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This work is licensed under a Creative Commons Attribution 3.0 License.

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