Mathematics – Representation Theory
Scientific paper
2007-11-07
J. Algebra 320(6):2363-2387, 2008
Mathematics
Representation Theory
17 pages, hyper-linked. Various typos and formatting corrected, final version
Scientific paper
10.1016/j.jalgebra.2008.06.011
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 lambda-ring homomorphisms.
No associations
LandOfFree
The rank of a quiver representation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The rank of a quiver representation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The rank of a quiver representation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-502806