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Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank

Steven P. Diaz·Mark Kleiner
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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.

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BibTeXRIS

Steven P. Diaz, Mark Kleiner. 2005-12-30. Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank. https://arxiv.org/abs/math/0512661

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