English

Dimension vectors in regular components over wild Kronecker quivers

Representation Theory 2012-09-05 v1

Abstract

Let Kn\mathcal{K}_n be the so-called wild Kronecker quiver, i.e., a quiver with one source and one sink and n3n\geq 3 arrows from the source to the sink. The following problems will be studied for an arbitrary regular component C\mathcal{C} of the Auslander-Reiten quiver: (1) What is the relationship between dimension vectors and quasi-lengths of the indecomposable regular representations in C\mathcal{C}? (2) For a given natural number dd, is there an upper bound of the number of indecomposable representations in C\mathcal{C} with the same length dd? (3) When do the sets of the dimension vectors of indecomposable representations in different regular components coincide?

Keywords

Cite

@article{arxiv.1209.0612,
  title  = {Dimension vectors in regular components over wild Kronecker quivers},
  author = {Bo Chen},
  journal= {arXiv preprint arXiv:1209.0612},
  year   = {2012}
}

Comments

19 pages

R2 v1 2026-06-21T21:59:28.728Z