Title
Qurves and quivers Qurves and quivers
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Journal of algebra. - New York, N.Y.
Volume/pages
290(2005) :2 , p. 447-472
ISSN
0021-8693
ISI
000230853100007
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this paper we associate to a View the MathML source-qurve A (formerly known as a quasi-free algebra [J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251289] or formally smooth algebra [M. Kontsevich, A. Rosenberg, Noncommutative smooth spaces, math.AG/9812158, 1998]) the one-quiver Q1(A) and dimension vector α1(A). This pair contains enough information to reconstruct for all View the MathML source the GLn-étale local structure of the representation scheme repnA. 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 kG is a k-qurve. If char(k)=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 algebras of graphs of separable k-algebras, we state the results in this more general setting.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/cc78e2/41a15e10.pdf
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