---
res:
bibo_abstract:
- In this paper we investigate locally free representations of a quiver Q over a
commutative Frobenius algebra R by arithmetic Fourier transform. When the base
field is finite we prove that the number of isomorphism classes of absolutely
indecomposable locally free representations of fixed rank is independent of the
orientation of Q. We also prove that the number of isomorphism classes of locally
free absolutely indecomposable representations of the preprojective algebra of
Q over R equals the number of isomorphism classes of locally free absolutely indecomposable
representations of Q over R[t]/(t2). Using these results together with results
of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification
of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally
free representations of Q over R is finite. Finally when the representation is
free of rank 1 at each vertex of Q, we study the function that counts the number
of isomorphism classes of absolutely indecomposable locally free representations
of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial
in q and their generating function is rational and satisfies a functional equation.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Tamás
foaf_name: Hausel, Tamás
foaf_surname: Hausel
foaf_workInfoHomepage: http://www.librecat.org/personId=4A0666D8-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Emmanuel
foaf_name: Letellier, Emmanuel
foaf_surname: Letellier
- foaf_Person:
foaf_givenName: Fernando
foaf_name: Rodriguez-Villegas, Fernando
foaf_surname: Rodriguez-Villegas
bibo_doi: 10.1007/s00029-023-00914-2
bibo_issue: '2'
bibo_volume: 30
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/1022-1824
- http://id.crossref.org/issn/1420-9020
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Locally free representations of quivers over commutative Frobenius algebras@
...