Article ID Journal Published Year Pages File Type
4588177 Journal of Algebra 2008 25 Pages PDF
Abstract

We define a functor which gives the “global rank of a quiver representation” and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other “rank functors” for a quiver Q, which induce ring homomorphisms (called “rank functions”) from the representation ring of Q to Z. These rank functions give discrete numerical invariants of quiver representations, useful for computing tensor product multiplicities of representations and determining some structure of the representation ring. We also show that in characteristic 0, rank functors commute with the Schur operations on quiver representations, and the homomorphisms induced by rank functors are λ-ring homomorphisms.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory