Journal article
The rank of a quiver representation
Journal of algebra, Vol.320(6), pp.2363-2387
2008
DOI: 10.1016/j.jalgebra.2008.06.011
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.
Details
- Title: Subtitle
- The rank of a quiver representation
- Creators
- Ryan Kinser - Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.320(6), pp.2363-2387
- DOI
- 10.1016/j.jalgebra.2008.06.011
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2008
- Academic Unit
- Mathematics
- Record Identifier
- 9983985956702771
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