Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank
Representation Theory
2007-05-23 v1 Commutative Algebra
Algebraic Geometry
Abstract
With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the multiplication maps in the commutative polynomial ring. The result follows from a more general theorem about the maximal rank property of a minimal almost split morphism, which also yields a quadratic inequality for the dimensions of indecomposable modules involved.
Keywords
Cite
@article{arxiv.math/0512661,
title = {Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank},
author = {Steven P. Diaz and Mark Kleiner},
journal= {arXiv preprint arXiv:math/0512661},
year = {2007}
}