|
Title
|
|
|
|
Qurves and quivers
| |
|
Author
|
|
|
|
| |
|
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. |
| |
|
Language
|
|
|
|
English
| |
|
Source (journal)
|
|
|
|
Journal of algebra. - New York, N.Y., 1964, currens
| |
|
Publication
|
|
|
|
New York, N.Y.
:
Academic Press
,
2005
| |
|
ISSN
|
|
|
|
0021-8693
| |
|
DOI
|
|
|
|
10.1016/J.JALGEBRA.2005.05.012
| |
|
Volume/pages
|
|
|
|
290
:2
(2005)
, p. 447-472
| |
|
ISI
|
|
|
|
000230853100007
| |
|
Full text (Publisher's DOI)
|
|
|
|
| |
|
Full text (open access)
|
|
|
|
| |
|