Title
Qurves and quivers Qurves and quivers
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
eprint-archive math.RA
Volume/pages
(2004) , p. 0507494,1-0507494,22
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
In this paper we associate to a qurve A (formerly known as a quasi-free or formally smooth algebra) the one-quiver Q(A) and dimension vector a(A). This pair contains enough information to reconstruct for all natural numbers n the GL(n)-etale local structure of the representation scheme rep(n,A). In an appendix we indicate how one might extend this to qurves over non-algebraically closed fields. Further, we classify all finitely generated groups G such that the group algebra lG is an l-qurve. If char(l)=0 these are exactly the virtually free groups. We determine the one-quiver setting in this case and indicate how it can be used to study the finite dimensional representations of virtually free groups. As this approach also applies to fundamental algbras of graphs of separable l-algebras, we state the results in this more general setting.
E-info
http://arxiv.org/abs/math.RA/0406618
Handle